A022604 Expansion of Product_{m>=1} (1+q^m)^(-9).

1, -9, 36, -93, 207, -459, 957, -1827, 3357, -6061, 10620, -18045, 30006, -49122, 79128, -125247, 195435, -301599, 460167, -694026, 1036368, -1534305, 2252277, -3278709, 4736973, -6797196, 9689103, -13722487

Offset

0,2

Links

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

Formula

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

a(0) = 1, a(n) = -(9/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017

G.f.: exp(-9*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^9, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Crossrefs

Column k=9 of A286352.

Sequence in context: A342252 A226253 A340965 * A085630 A133226 A027602

Adjacent sequences: A022601 A022602 A022603 * A022605 A022606 A022607

Keyword

sign

Author

N. J. A. Sloane

Status

approved