A022615 Expansion of Product_{m>=1} (1+q^m)^(-20).

1, -20, 190, -1160, 5245, -19324, 62150, -182040, 495750, -1269620, 3088376, -7197240, 16164595, -35136760, 74192590, -152674048, 306968470, -604298520, 1166898210, -2213813640, 4132159452, -7597272900

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)^20, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

a(n) ~ (-1)^n * 5^(1/4) * exp(Pi*sqrt(10*n/3)) / (2 * 6^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

a(0) = 1, a(n) = -(20/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017