|
|
A022602
|
|
Expansion of Product_{m>=1} (1+q^m)^(-7).
|
|
4
|
|
|
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
|
|
|
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
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
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|