Search: a052893 -id:a052893
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A277996
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Number of free pure symmetric multifunctions (with empty expressions allowed) with one atom and n positions.
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+10
33
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1, 1, 2, 5, 13, 36, 102, 299, 892, 2713, 8364, 26108, 82310, 261804, 838961, 2706336, 8780725, 28636157, 93818641, 308641277, 1019140129, 3376604826, 11221805968, 37399728251, 124967677989, 418564867751, 1405030366113, 4726036692421, 15927027834163, 53770343259613
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OFFSET
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1,3
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COMMENTS
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Also the number of distinct orderless Mathematica expressions with one atom and n positions.
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(x) = x * (1 + A(x) * exp(Sum_{k>=1} A(x^k)/k)).
G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * (1 + (Sum_{n>=1} a(n)*x^n) * Product_{n>=1} 1/(1 - x^n)^a(n)). (End)
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EXAMPLE
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The a(5)=13 Mathematica expressions are:
x[x,x,x]
x[x,x][] x[x][x] x[][x,x] x[x,x[]] x[x[x]]
x[x][][] x[][x][] x[][][x] x[x[]][] x[][x[]] x[x[][]]
x[][][][]
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MATHEMATICA
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multing[t_, n_]:=Array[(t+#-1)/#&, n, 1, Times];
a[n_]:=a[n]=If[n===1, 1, Sum[a[k]*Sum[Product[multing[a[First[s]], Length[s]], {s, Split[p]}], {p, IntegerPartitions[n-k-1]}], {k, 1, n-1}]];
Array[a, 30]
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PROG
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(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(v=[1]); for(n=2, n, my(t=EulerT(v)); v=concat(v, v[n-1] + sum(k=1, n-2, v[k]*t[n-k-1]))); v} \\ Andrew Howroyd, Aug 19 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A317658
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Number of positions in the n-th free pure symmetric multifunction (with empty expressions allowed) with one atom.
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+10
16
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1, 2, 3, 3, 4, 4, 5, 4, 4, 5, 6, 5, 5, 6, 7, 4, 6, 6, 7, 8, 5, 7, 7, 8, 5, 9, 5, 6, 8, 8, 9, 5, 6, 10, 6, 5, 7, 9, 9, 10, 6, 7, 11, 7, 6, 8, 10, 10, 6, 11, 7, 8, 12, 8, 7, 9, 11, 11, 7, 12, 8, 9, 13, 5, 9, 8, 10, 12, 12, 8, 13, 9, 10, 14, 6, 10, 9, 11, 13, 13
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OFFSET
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1,2
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COMMENTS
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Given a positive integer n > 1 we construct a unique free pure symmetric multifunction e(n) by expressing n as a power of a number that is not a perfect power to a product of prime numbers: n = rad(x)^(prime(y_1) * ... * prime(y_k)) where rad = A007916. Then e(n) = e(x)[e(y_1), ..., e(y_k)].
Also the number of positions in the orderless Mathematica expression with e-number n.
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LINKS
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FORMULA
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a(rad(x)^(prime(y_1) * ... * prime(y_k)) = a(x) + a(y_1) + ... + a(y_k).
e(2^(2^n)) = o[o,...,o].
e(2^prime(2^prime(2^...))) = o[o[...o[o]]].
e(rad(rad(rad(...)^2)^2)^2) = o[o][o]...[o].
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EXAMPLE
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The first twenty Mathematica expressions:
1: o
2: o[]
3: o[][]
4: o[o]
5: o[][][]
6: o[o][]
7: o[][][][]
8: o[o[]]
9: o[][o]
10: o[o][][]
11: o[][][][][]
12: o[o[]][]
13: o[][o][]
14: o[o][][][]
15: o[][][][][][]
16: o[o,o]
17: o[o[]][][]
18: o[][o][][]
19: o[o][][][][]
20: o[][][][][][][]
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MATHEMATICA
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nn=100;
radQ[n_]:=If[n===1, False, GCD@@FactorInteger[n][[All, 2]]===1];
rad[n_]:=rad[n]=If[n===0, 1, NestWhile[#+1&, rad[n-1]+1, Not[radQ[#]]&]];
Clear[radPi]; Set@@@Array[radPi[rad[#]]==#&, nn];
exp[n_]:=If[n===1, x, With[{g=GCD@@FactorInteger[n][[All, 2]]}, Apply[exp[radPi[Power[n, 1/g]]], exp/@Flatten[Cases[FactorInteger[g], {p_?PrimeQ, k_}:>ConstantArray[PrimePi[p], k]]]]]];
Table[exp[n], {n, 1, nn}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A317875
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Number of achiral free pure multifunctions with n unlabeled leaves.
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+10
13
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1, 1, 3, 9, 30, 102, 369, 1362, 5181, 20064, 79035, 315366, 1272789, 5185080, 21296196, 88083993, 366584253, 1533953100, 6449904138, 27238006971, 115475933202, 491293053093, 2096930378415, 8976370298886, 38528771056425, 165784567505325
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OFFSET
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1,3
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COMMENTS
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An achiral free pure multifunction is either (case 1) the leaf symbol "o", or (case 2) a nonempty expression of the form h[g, ..., g], where h and g are both achiral free pure multifunctions.
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LINKS
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FORMULA
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a(1) = 1; a(n > 1) = Sum_{0 < k < n} a(n - k) * Sum_{d|k} a(d).
G.f. A(x) satisfies: A(x) = x + A(x) * Sum_{k>=1} A(x^k).
G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x + (Sum_{n>=1} a(n)*x^n) * (Sum_{n>=1} a(n)*x^n/(1 - x^n)). (End)
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EXAMPLE
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The first 4 terms count the following multifunctions.
o,
o[o],
o[o,o], o[o[o]], o[o][o],
o[o,o,o], o[o[o][o]], o[o[o[o]]], o[o[o,o]], o[o][o,o], o[o][o[o]], o[o][o][o], o[o,o][o], o[o[o]][o].
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MATHEMATICA
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a[n_]:=If[n==1, 1, Sum[a[n-k]*Sum[a[d], {d, Divisors[k]}], {k, n-1}]];
Array[a, 12]
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PROG
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(PARI) seq(n)={my(p=O(x)); for(n=1, n, p = x + p*(sum(k=1, n-1, subst(p + O(x^(n\k+1)), x, x^k)) ) + O(x*x^n)); Vec(p)} \\ Andrew Howroyd, Aug 19 2018
(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n]=sum(i=1, n-1, v[i]*sumdiv(n-i, d, v[d]))); v} \\ Andrew Howroyd, Aug 19 2018
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CROSSREFS
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Cf. A001003, A001678, A002033, A003238, A052893, A053492, A067824, A167865, A214577, A277996, A280000, A317853.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A317654
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Number of free pure symmetric multifunctions whose leaves are a strongly normal multiset of size n.
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+10
10
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1, 3, 26, 375, 6696, 159837, 4389226, 144915350, 5377002075, 227624621051, 10632808475596, 550932945236121, 31062550998284221, 1907051034025848314, 126052420069459211076, 8956882232940915920404, 679298518935625486287703, 54868537321267493152151502, 4696952405203792017289469056
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OFFSET
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1,2
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COMMENTS
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A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities. A free pure symmetric multifunction f in EPSM is either (case 1) a positive integer, or (case 2) an expression of the form h[g_1, ..., g_k] where k > 0, h is in EPSM, each of the g_i for i = 1, ..., k is in EPSM, and for i < j we have g_i <= g_j under a canonical total ordering of EPSM, such as the Mathematica ordering of expressions.
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LINKS
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EXAMPLE
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The a(3) = 26 free pure symmetric multifunctions:
1[1[1]], 1[1,1], 1[1][1],
1[1[2]], 1[2[1]], 1[1,2], 2[1[1]], 2[1,1], 1[1][2], 1[2][1], 2[1][1],
1[2[3]], 1[3[2]], 1[2,3], 2[1[3]], 2[3[1]], 2[1,3], 3[1[2]], 3[2[1]], 3[1,2], 1[2][3], 2[1][3], 1[3][2], 3[1][2], 2[3][1], 3[2][1].
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MATHEMATICA
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sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
exprUsing[m_]:=exprUsing[m]=If[Length[m]==0, {}, If[Length[m]==1, {First[m]}, Join@@Cases[Union[Table[PR[m[[s]], m[[Complement[Range[Length[m]], s]]]], {s, Take[Subsets[Range[Length[m]]], {2, -2}]}]], PR[h_, g_]:>Join@@Table[Apply@@@Tuples[{exprUsing[h], Union[Sort/@Tuples[exprUsing/@p]]}], {p, mps[g]}]]]];
got[y_]:=Join@@Table[Table[i, {y[[i]]}], {i, Range[Length[y]]}];
Table[Sum[Length[exprUsing[got[y]]], {y, IntegerPartitions[n]}], {n, 6}]
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PROG
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(PARI) \\ See links in A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(p=O(x)); for(n=1, n, p = x*sv(1) + p*(sExp(p)-1)); p}
StronglyNormalLabelingsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Jan 01 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A317652
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Number of free pure symmetric multifunctions whose leaves are an integer partition of n.
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+10
9
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1, 1, 2, 6, 22, 93, 421, 2010, 9926, 50357, 260728, 1372436, 7321982, 39504181, 215168221, 1181540841, 6534058589, 36357935615, 203414689462, 1143589234086, 6457159029573, 36602333187792, 208214459462774, 1188252476400972, 6801133579291811, 39032172166792887
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OFFSET
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0,3
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COMMENTS
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A free pure symmetric multifunction f in EPSM is either (case 1) a positive integer, or (case 2) an expression of the form h[g_1, ..., g_k] where k > 0, h is in EPSM, each of the g_i for i = 1, ..., k is in EPSM, and for i < j we have g_i <= g_j under a canonical total ordering of EPSM, such as the Mathematica ordering of expressions.
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LINKS
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EXAMPLE
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The a(4) = 22 free pure symmetric multifunctions:
1[1[1[1]]] 1[1[2]] 1[3] 2[2] 4
1[1[1][1]] 1[2[1]] 3[1]
1[1][1[1]] 2[1[1]]
1[1[1]][1] 1[1][2]
1[1][1][1] 1[2][1]
1[1[1,1]] 2[1][1]
1[1,1[1]] 1[1,2]
1[1][1,1] 2[1,1]
1[1,1][1]
1[1,1,1]
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MATHEMATICA
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sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
exprUsing[m_]:=exprUsing[m]=If[Length[m]==0, {{}}, If[Length[m]==1, {First[m]}, Join@@Cases[Union[Table[PR[m[[s]], m[[Complement[Range[Length[m]], s]]]], {s, Take[Subsets[Range[Length[m]]], {2, -2}]}]], PR[h_, g_]:>Join@@Table[Apply@@@Tuples[{exprUsing[h], Union[Sort/@Tuples[exprUsing/@p]]}], {p, mps[g]}]]]];
Table[Sum[Length[exprUsing[y]], {y, IntegerPartitions[n]}], {n, 0, 6}]
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PROG
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(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(v=[]); for(n=1, n, my(t=EulerT(v)); v=concat(v, 1 + sum(k=1, n-1, v[k]*t[n-k]))); concat([1], v)} \\ Andrew Howroyd, Aug 28 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A317653
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Number of free pure symmetric multifunctions whose leaves are a normal multiset of size n.
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+10
9
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1, 3, 34, 602, 14872, 472138, 18323359, 840503724, 44489123726, 2668985463839, 178960530393633, 13263068003965046, 1076580864432281157, 94987639225399100006, 9051397653144246683937, 926407121115738135640677, 101357200280211387377806719, 11804887470887800839909147484
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OFFSET
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1,2
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COMMENTS
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A multiset is normal if it spans an initial interval of positive integers. A free pure symmetric multifunction f in EPSM is either (case 1) a positive integer, or (case 2) an expression of the form h[g_1, ..., g_k] where k > 0, h is in EPSM, each of the g_i for i = 1, ..., k is in EPSM, and for i < j we have g_i <= g_j under a canonical total ordering of EPSM, such as the Mathematica ordering of expressions.
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LINKS
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EXAMPLE
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The a(3) = 34 free pure symmetric multifunctions:
1[1[1]], 1[1,1], 1[1][1],
1[2[2]], 1[2,2], 2[1[2]], 2[2[1]], 2[1,2], 1[2][2], 2[1][2], 2[2][1],
1[1[2]], 1[2[1]], 1[1,2], 2[1[1]], 2[1,1], 1[1][2], 1[2][1], 2[1][1],
1[2[3]], 1[3[2]], 1[2,3], 2[1[3]], 2[3[1]], 2[1,3], 3[1[2]], 3[2[1]], 3[1,2], 1[2][3], 2[1][3], 1[3][2], 3[1][2], 2[3][1], 3[2][1].
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MATHEMATICA
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sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
exprUsing[m_]:=exprUsing[m]=If[Length[m]==0, {}, If[Length[m]==1, {First[m]}, Join@@Cases[Union[Table[PR[m[[s]], m[[Complement[Range[Length[m]], s]]]], {s, Take[Subsets[Range[Length[m]]], {2, -2}]}]], PR[h_, g_]:>Join@@Table[Apply@@@Tuples[{exprUsing[h], Union[Sort/@Tuples[exprUsing/@p]]}], {p, mps[g]}]]]];
got[y_]:=Join@@Table[Table[i, {y[[i]]}], {i, Range[Length[y]]}];
Table[Sum[Length[exprUsing[got[y]]], {y, Join@@Permutations/@IntegerPartitions[n]}], {n, 6}]
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PROG
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EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
R(n, k)={my(v=[k]); for(n=2, n, my(t=EulerT(v)); v=concat(v, sum(k=1, n-1, v[k]*t[n-k]))); v}
seq(n)={sum(k=1, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) )} \\ Andrew Howroyd, Sep 14 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A317876
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Number of free pure symmetric identity multifunctions (with empty expressions allowed) with one atom and n positions.
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+10
8
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1, 1, 2, 4, 10, 25, 67, 184, 519, 1489, 4342, 12812, 38207, 114934, 348397, 1063050, 3262588, 10064645, 31190985, 97061431, 303165207, 950115502, 2986817742, 9415920424, 29760442192, 94286758293, 299377379027, 952521579944, 3036380284111, 9696325863803
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OFFSET
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1,3
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COMMENTS
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A free pure symmetric identity multifunction (with empty expressions allowed) (FOI) is either (case 1) the leaf symbol "o", or (case 2) a possibly empty expression of the form h[g_1, ..., g_k] where h is an FOI, each of the g_i for i = 1, ..., k >= 0 is an FOI, and for i < j we have g_i < g_j under a canonical total ordering such as the Mathematica ordering of expressions. The number of positions in an FOI is the number of brackets [...] plus the number of o's.
Also the number of free orderless identity Mathematica expressions with one atom and n positions.
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(x) = x * (1 + A(x) * exp(Sum_{k>=1} (-1)^(k+1)*A(x^k)/k)).
G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * (1 + (Sum_{n>=1} a(n)*x^n) * Product_{n>=1} (1 + x^n)^a(n)). (End)
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EXAMPLE
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The a(5) = 10 FOIs:
o[o[o]]
o[o][o]
o[o[][]]
o[o,o[]]
o[][o[]]
o[][][o]
o[o[]][]
o[][o][]
o[o][][]
o[][][][]
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MATHEMATICA
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allIdExpr[n_]:=If[n==1, {"o"}, Join@@Cases[Table[PR[k, n-k-1], {k, n-1}], PR[h_, g_]:>Join@@Table[Apply@@@Tuples[{allIdExpr[h], Select[Union[Sort/@Tuples[allIdExpr/@p]], UnsameQ@@#&]}], {p, IntegerPartitions[g]}]]];
Table[Length[allIdExpr[n]], {n, 12}]
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PROG
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(PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
seq(n)={my(v=[1]); for(n=2, n, my(t=WeighT(v)); v=concat(v, v[n-1] + sum(k=1, n-2, v[k]*t[n-k-1]))); v} \\ Andrew Howroyd, Aug 19 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A317877
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Number of free pure identity multifunctions with one atom and n positions.
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+10
8
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1, 0, 1, 0, 2, 2, 5, 10, 18, 46, 94, 212, 476, 1058, 2441, 5564, 12880, 29920, 69620, 163220, 383376, 904114, 2139592, 5074784, 12074152, 28789112, 68803148, 164779064, 395373108, 950416330, 2288438591, 5518864858, 13329183894, 32237132814, 78069124640
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OFFSET
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1,5
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COMMENTS
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A free pure identity multifunction (PIM) is either (case 1) the leaf symbol "o", or (case 2) an expression of the form h[g_1, ..., g_k] where h is a PIM, each of the g_i for i = 1, ..., k > 0 is a PIM, and for i != j we have g_i != g_j. The number of positions in a PIM is the number of brackets [...] plus the number of o's.
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LINKS
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EXAMPLE
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The a(8) = 10 PIMs:
o[o[o[o],o]]
o[o[o,o[o]]]
o[o[o[o]],o]
o[o[o][o],o]
o[o,o[o[o]]]
o[o,o[o][o]]
o[o][o[o],o]
o[o][o,o[o]]
o[o[o],o][o]
o[o,o[o]][o]
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MATHEMATICA
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allIdPMF[n_]:=If[n==1, {"o"}, Join@@Cases[Table[PR[k, n-k-1], {k, n-2}], PR[h_, g_]:>Join@@Table[Apply@@@Tuples[{allIdPMF[h], Select[Tuples[allIdPMF/@p], UnsameQ@@#&]}], {p, Join@@Permutations/@IntegerPartitions[g]}]]];
Table[Length[allIdPMF[n]], {n, 12}]
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PROG
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(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, n, my(p=prod(k=1, n, 1 + sum(i=1, n\k, binomial(v[k], i)*x^(i*k)*y^i) + O(x*x^n))); v[n]=sum(k=1, n-2, v[n-k-1]*subst(serlaplace(y^0*polcoef(p, k)), y, 1))); v} \\ Andrew Howroyd, Sep 01 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A317878
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Number of free pure symmetric identity multifunctions with one atom and n positions.
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+10
8
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1, 0, 1, 0, 2, 1, 5, 5, 15, 23, 54, 98, 212, 420, 886, 1822, 3838, 8046, 17029, 36097, 76889, 164245, 351971, 756341, 1629389, 3518643, 7614717, 16512962, 35875986, 78082171, 170219300, 371651968, 812624721, 1779240627, 3900634491, 8561723769, 18814112811
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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A free pure symmetric identity multifunction (SIM) is either (case 1) the leaf symbol "o", or (case 2) an expression of the form h[g_1, ..., g_k] where h is a SIM, each of the g_i for i = 1, ..., k > 0 is a SIM, and for i < j we have g_i < g_j under a canonical total ordering such as the Mathematica ordering of expressions. The number of positions in a SIM is the number of brackets [...] plus the number of o's.
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LINKS
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EXAMPLE
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The a(8) = 5 SIMs:
o[o[o,o[o]]]
o[o,o[o[o]]]
o[o,o[o][o]]
o[o][o,o[o]]
o[o,o[o]][o]
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MATHEMATICA
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allIdPMFOL[n_]:=If[n==1, {"o"}, Join@@Cases[Table[PR[k, n-k-1], {k, n-2}], PR[h_, g_]:>Join@@Table[Apply@@@Tuples[{allIdPMFOL[h], Select[Union[Sort/@Tuples[allIdPMFOL/@p]], UnsameQ@@#&]}], {p, IntegerPartitions[g]}]]];
Table[Length[allIdPMFOL[n]], {n, 12}]
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PROG
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(PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
seq(n)={my(v=[1]); for(n=2, n, my(t=WeighT(v)); v=concat(v, sum(k=1, n-2, v[k]*t[n-k-1]))); v} \\ Andrew Howroyd, Aug 19 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A317880
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Number of series-reduced free pure symmetric identity multifunctions (with empty expressions allowed) with one atom and n positions.
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+10
8
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1, 1, 1, 1, 2, 4, 8, 16, 33, 70, 152, 333, 735, 1635, 3668, 8285, 18823, 42970, 98535, 226870, 524290, 1215641, 2827203, 6593432, 15416197, 36129894, 84860282, 199719932, 470930802, 1112388190, 2631903295, 6236669381, 14800078408, 35169529363, 83680908692
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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A series-reduced free pure symmetric identity multifunction (with empty expressions allowed) (SROI) is either (case 1) the leaf symbol "o", or (case 2) a possibly empty expression of the form h[g_1, ..., g_k] where h is an SROI, k is an integer greater than or equal to 0 but not equal to 1, each of the g_i for i = 1, ..., k is an SROI, and for i < j we have g_i < g_j under a canonical total ordering such as the Mathematica ordering of expressions. The number of positions in an SROI is the number of brackets [...] plus the number of o's.
Also the number of series-reduced orderless identity Mathematica expressions with one atom and n positions.
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LINKS
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EXAMPLE
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The a(7) = 8 SROIs:
o[o,o[][][]]
o[o[],o[][]]
o[][o,o[][]]
o[][][o,o[]]
o[o,o[][]][]
o[][o,o[]][]
o[o,o[]][][]
o[][][][][][]
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MATHEMATICA
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allIdExprSR[n_]:=If[n==1, {"o"}, Join@@Cases[Table[PR[k, n-k-1], {k, n-1}], PR[h_, g_]:>Join@@Table[Apply@@@Tuples[{allIdExprSR[h], Select[Union[Sort/@Tuples[allIdExprSR/@p]], UnsameQ@@#&]}], {p, If[g==0, {{}}, Rest[IntegerPartitions[g]]]}]]];
Table[Length[allIdExprSR[n]], {n, 12}]
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PROG
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(PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
seq(n)={my(v=[1]); for(n=2, n, my(t=WeighT(v)-v); v=concat(v, v[n-1] + sum(k=1, n-2, v[k]*t[n-k-1]))); v} \\ Andrew Howroyd, Aug 19 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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