A022731 Expansion of Product_{m>=1} 1/(1 - m*q^m)^7.

1, 7, 42, 203, 889, 3535, 13209, 46551, 156905, 507787, 1588594, 4819003, 14231294, 41007134, 115589904, 319284693, 865781826, 2307766118, 6054769679, 15652436765, 39909873983, 100451866962

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=7 of A297328.

Programs

Magma

n:=50; R:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^7:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-7, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 25 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-7)) \\ G. C. Greubel, Jul 25 2018

Formula

G.f.: exp(7*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018