A022626 Expansion of Product_{m>=1} (1+q^m)^(-31).

1, -31, 465, -4526, 32426, -184357, 877052, -3633851, 13513458, -46099108, 146495398, -438514468, 1246964119, -3391183930, 8867709030, -22393552057, 54808232438, -130404256148, 302394884204, -684929956630, 1518203338688

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

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

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^31, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

a(n) ~ (-1)^n * 31^(1/4) * exp(Pi*sqrt(31*n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015