A022605 Expansion of Product_{m>=1} (1+q^m)^(-10).

1, -10, 45, -130, 310, -712, 1555, -3130, 5990, -11190, 20316, -35750, 61405, -103570, 171730, -279782, 448785, -710830, 1112515, -1720550, 2632389, -3989480, 5992085, -8921670, 13176300, -19316144, 28118360, -40654520

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^10, {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/3)) / (2^(3/2) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

a(0) = 1, a(n) = -(10/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017