A022620 Expansion of Product_{m>=1} (1+q^m)^(-25).

1, -25, 300, -2325, 13275, -60655, 235525, -811975, 2558575, -7502175, 20713560, -54345175, 136483700, -329961200, 771284950, -1749490965, 3862641850, -8322360350, 17536187475, -36204137625, 73353404555, -146061623800, 286183499350, -552361219950, 1051231017350

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)^25, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

a(n) ~ (-1)^n * sqrt(5) * exp(5*Pi*sqrt(n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015