A022614 Expansion of Product_{m>=1} (1+q^m)^(-19).

1, -19, 171, -988, 4237, -14896, 46075, -130549, 344888, -858325, 2032924, -4621313, 10137716, -21545639, 44525987, -89757843, 176925625, -341688495, 647687314, -1206921212, 2213842874, -4001882220, 7136374179

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)^19, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

a(n) ~ (-1)^n * 19^(1/4) * exp(Pi*sqrt(19*n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

a(0) = 1, a(n) = -(19/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017