Revision History for A115625
(Underlined text is an addition;
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Showing entries 1-10
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#12 by Alois P. Heinz at Fri Apr 21 14:31:10 EDT 2023
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#11 by Alois P. Heinz at Fri Apr 21 14:31:08 EDT 2023
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# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add((j->
a(n-j)*binomial(n-1, j-1))(2^i), i=0..ilog2(n)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Apr 21 2023
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approved
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#10 by Alois P. Heinz at Thu Oct 29 08:05:59 EDT 2015
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#9 by Jean-François Alcover at Thu Oct 29 07:29:41 EDT 2015
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#8 by Jean-François Alcover at Thu Oct 29 07:29:34 EDT 2015
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| MATHEMATICA
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multinomial[n_, k_List] := n!/Times @@ (k!); !); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*b[n - i*j, i/2], {j, 0, n/i}]]]; a[n_] := b[n, 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Oct 29 2015, after _Alois P. Heinz_ *)
b[n_, i_] :=
b[n, i] =
If[n == 0, 1,
If[i < 1, 0,
Sum[multinomial[n, Join[{ n - i*j}, Array[i &, j]]]/j!*
b[n - i*j, i/2], {j, 0, n/i}]]] ;
a[n_] := b[n, 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 30}]
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#7 by Jean-François Alcover at Thu Oct 29 07:27:07 EDT 2015
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| MATHEMATICA
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multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] :=
b[n, i] =
If[n == 0, 1,
If[i < 1, 0,
Sum[multinomial[n, Join[{ n - i*j}, Array[i &, j]]]/j!*
b[n - i*j, i/2], {j, 0, n/i}]]] ;
a[n_] := b[n, 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 30}]
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approved
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#6 by Alois P. Heinz at Thu Sep 17 16:16:06 EDT 2015
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#5 by Alois P. Heinz at Thu Sep 17 16:16:03 EDT 2015
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| LINKS
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Alois P. Heinz, <a href="/A115625/b115625.txt">Table of n, a(n) for n = 0..604</a>
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#4 by Alois P. Heinz at Thu Sep 17 16:15:47 EDT 2015
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| MAPLE
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with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i/2), j=0..n/i)))
end:
a:= n-> b(n, 2^ilog2(n)):
seq(a(n), n=0..30); # Alois P. Heinz, Sep 17 2015
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#3 by Alois P. Heinz at Thu Sep 17 16:12:30 EDT 2015
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| DATA
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1, 1, 2, 4, 11, 31, 106, 372, 1500, 6220, 28696, 136016, 702802, 3727946, 21253324, 124231096, 772458367, 4918962479, 33061095118, 227303570524, 1639389365201, 12082068856285, 92951844299150, 729991789222972, 5960617085224012, 49637008114202876
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approved
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