A022699 Expansion of Product_{m>=1} 1/(1 + m*q^m)^7.

1, -7, 14, -7, 49, -203, 217, -295, 1365, -2667, 4214, -8519, 16842, -38570, 69012, -104433, 240758, -493374, 786835, -1434601, 2842567, -5272206, 9205546, -16034312, 29916572, -55466005, 95595395, -163656780

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=7 of A297325.

Programs

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-7, {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)^-7)) \\ G. C. Greubel, Jul 19 2018

Formula

G.f.: exp(-7*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018