A022609 Expansion of Product_{m>=1} (1+q^m)^(-14).

1, -14, 91, -378, 1197, -3290, 8386, -20008, 44800, -95578, 196679, -391692, 756798, -1424934, 2624119, -4735878, 8388919, -14611226, 25065397, -42400456, 70790195, -116765126, 190454404, -307408346, 491306907

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)^14, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

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

a(0) = 1, a(n) = -(14/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017