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A022604 Expansion of Product_{m>=1} (1+q^m)^(-9). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A162258 A128642 A226253 * A085630 A133226 A027602

Adjacent sequences:  A022601 A022602 A022603 * A022605 A022606 A022607

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)