A022602 Expansion of Product_{m>=1} (1+q^m)^(-7).

1, -7, 21, -42, 84, -175, 322, -547, 931, -1561, 2527, -3976, 6167, -9485, 14336, -21280, 31304, -45696, 65940, -94122, 133371, -187734, 262143, -363265, 500381, -685503, 933506, -1263794, 1702590, -2283379, 3047597

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

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

Crossrefs

Column k=7 of A286352.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^7, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

PARI

x='x+O('x^50); Vec(prod(m=1, 50, (1 + x^m)^(-7))) \\ Indranil Ghosh, Apr 05 2017

Formula

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

a(0) = 1, a(n) = -(7/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017

G.f.: exp(-7*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018