A022700 Expansion of Product_{m>=1} 1/(1 + m*q^m)^8.

1, -8, 20, -16, 58, -288, 424, -464, 2035, -4816, 7364, -15008, 32030, -69152, 135352, -217840, 460537, -1012000, 1704176, -3043120, 6200086, -11737792, 21029184, -37602016, 70312646, -132822480, 235883988, -412277440

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

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

Crossrefs

Column k=8 of A297325.

Programs

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-8, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 19 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^-8)) \\ G. C. Greubel, Jul 19 2018

Formula

G.f.: exp(-8*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018