A022616 Expansion of Product_{m>=1} (1+q^m)^(-21).

1, -21, 210, -1351, 6426, -24780, 82845, -250806, 703731, -1853481, 4628337, -11052867, 25403952, -56451192, 121738767, -255623851, 524037507, -1051143723, 2066899387, -3990768663, 7577013360, -14163858895

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)^21, {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/2)) / (2^(7/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

a(0) = 1, a(n) = -(21/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017