A022627 Expansion of Product_{m>=1} (1+q^m)^(-32).

1, -32, 496, -4992, 36984, -217280, 1066432, -4548352, 17369116, -60711456, 197327712, -603261056, 1749861312, -4849210560, 12909347456, -33162318080, 82507571334, -199432268416, 469559849680, -1079335967872

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Comments

In general, for k > 0, if g.f. = Product_{m>=1} 1/(1+q^m)^k, then a(n) ~ (-1)^n * exp(Pi*sqrt(k*n/6)) * k^(1/4) / (2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^32, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

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