A022611 Expansion of Product_{m>=1} (1+q^m)^(-16).

1, -16, 120, -576, 2076, -6304, 17344, -44416, 106630, -242480, 528608, -1112128, 2265656, -4486112, 8666112, -16376192, 30328593, -55145872, 98613424, -173670400, 301550788, -516747872, 874774016, -1464096000

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

Links

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

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^16, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

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

a(0) = 1, a(n) = -(16/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017