A022610 Expansion of Product_{m>=1} (1+q^m)^(-15).

1, -15, 105, -470, 1590, -4593, 12160, -30075, 69780, -153750, 325728, -667020, 1323915, -2557140, 4824630, -8912759, 16148505, -28746945, 50364835, -86956260, 148098384, -249060745, 413975085, -680602545

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Comments

a(0) = 1, a(n) = -(15/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017

Links

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

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^15, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

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