A022608 Expansion of Product_{m>=1} (1+q^m)^(-13).

1, -13, 78, -299, 884, -2314, 5681, -13052, 28158, -58136, 116129, -224692, 422214, -774372, 1390948, -2450565, 4240561, -7221383, 12121980, -20076953, 32836752, -53089309, 84922877, -134488770, 210979548

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ (-1)^n * 13^(1/4) * exp(Pi*sqrt(13*n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

a(0) = 1, a(n) = -(13/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Crossrefs

Sequence in context: A194713 A047638 A010929 * A060216 A041318 A142056

Adjacent sequences: A022605 A022606 A022607 * A022609 A022610 A022611

Keyword

sign

Author

N. J. A. Sloane

Status

approved