Revision History for A317875
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#11 by Susanna Cuyler at Tue Apr 30 21:50:19 EDT 2019
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#10 by Ilya Gutkovskiy at Tue Apr 30 13:34:12 EDT 2019
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#9 by Ilya Gutkovskiy at Tue Apr 30 13:00:34 EDT 2019
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| FORMULA
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From Ilya Gutkovskiy, Apr 30 2019: (Start)
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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approved
editing
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#8 by Alois P. Heinz at Sun Aug 19 17:22:41 EDT 2018
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#7 by Andrew Howroyd at Sun Aug 19 16:05:47 EDT 2018
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#6 by Andrew Howroyd at Sun Aug 19 14:10:58 EDT 2018
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| LINKS
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Andrew Howroyd, <a href="/A317875/b317875.txt">Table of n, a(n) for n = 1..200</a>
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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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| STATUS
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approved
editing
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#5 by Susanna Cuyler at Sun Aug 12 16:10:37 EDT 2018
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#4 by Gus Wiseman at Sat Aug 11 22:12:19 EDT 2018
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#3 by Gus Wiseman at Sat Aug 11 22:11:03 EDT 2018
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| DATA
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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, 714982199707464, 3090048533003520, 13381010231482248, 58050688206938904
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| CROSSREFS
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Cf. A317876, A317877, A317878, A317879, A317880, A317881.
Cf. A317882, A317883, A317884, A317885.
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#2 by Gus Wiseman at Thu Aug 09 19:05:01 EDT 2018
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| NAME
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allocatedNumber of achiral free pure multifunctions with forn Gusunlabeled Wisemanleaves.
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| DATA
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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, 714982199707464, 3090048533003520, 13381010231482248, 58050688206938904
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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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| FORMULA
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a(1) = 1; a(n > 1) = Sum_{0 < k < n} a(n - k) * Sum_{d|k} a(d).
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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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| 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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allocated
nonn
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| AUTHOR
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Gus Wiseman, Aug 09 2018
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| STATUS
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approved
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