A022697 Expansion of Product_{m>=1} 1/(1 + m*q^m)^5.

1, -5, 5, 0, 35, -76, 35, -155, 455, -720, 1369, -1935, 4415, -10405, 12990, -22512, 54405, -92480, 143150, -253015, 488512, -859795, 1377670, -2332365, 4276230, -7666511, 12092880, -19796225, 36845455, -62053775

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=5 of A297325.

Programs

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-5, {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)^-5)) \\ G. C. Greubel, Jul 19 2018

Formula

G.f.: exp(-5*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018