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A022602 Expansion of Product_{m>=1} (1+q^m)^(-7). 2
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 (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 * 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

MATHEMATICA

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

PROG

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

CROSSREFS

Column k=7 of A286352.

Sequence in context: A162818 A024966 A226252 * A054569 A077354 A246430

Adjacent sequences:  A022599 A022600 A022601 * A022603 A022604 A022605

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 22 03:20 EST 2019. Contains 329383 sequences. (Running on oeis4.)