A022736 Expansion of 1/Product_{m>=1} (1 - m*q^m)^12.

1, 12, 102, 688, 4029, 21156, 102246, 461448, 1967658, 7990996, 31110432, 116685288, 423366831, 1490904528, 5110173678, 17088259888, 55862240688, 178836472032, 561532752086, 1731639278904, 5250722230962

Offset

0,2

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 12, g(n) = n. - Seiichi Manyama, Aug 16 2023

Links

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Formula

a(0) = 1; a(n) = (12/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 16 2023

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-12, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 25 2018 *)

Prog

(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1-n*q^n)^-12)) \\ G. C. Greubel, Jul 25 2018
(Magma) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^12:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Crossrefs

Column k=12 of A297328.

Cf. A078308.

Sequence in context: A344366 A304504 A344279 * A261483 A082151 A125375

Adjacent sequences: A022733 A022734 A022735 * A022737 A022738 A022739

Keyword

nonn

Author

N. J. A. Sloane

Status

approved