A022622 Expansion of Product_{m>=1} (1+q^m)^(-27).

1, -27, 351, -2952, 18279, -90234, 376065, -1380861, 4603419, -14211732, 41168493, -112989411, 296067411, -745157691, 1809973404, -4259279106, 9741879531, -21715736634, 47285714262, -100777640049, 210581729640, -432065248731, 871606288422, -1730764207107, 3386501241606

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Programs

Mathematica

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

Formula

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