A022618 Expansion of Product_{m>=1} (1+q^m)^(-23).

1, -23, 253, -1794, 9384, -39491, 142462, -460483, 1370041, -3810479, 10013533, -25082512, 60303171, -139870107, 314254704, -686285914, 1461009887, -3039222369, 6190256915, -12366732828, 24269855093

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^23, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

a(n) ~ (-1)^n * 23^(1/4) * exp(Pi*sqrt(23*n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

a(0) = 1, a(n) = -(23/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017