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%I #20 Feb 06 2018 15:11:09
%S 1,-7,21,-42,84,-175,322,-547,931,-1561,2527,-3976,6167,-9485,14336,
%T -21280,31304,-45696,65940,-94122,133371,-187734,262143,-363265,
%U 500381,-685503,933506,-1263794,1702590,-2283379,3047597
%N Expansion of Product_{m>=1} (1+q^m)^(-7).
%H Seiichi Manyama, <a href="/A022602/b022602.txt">Table of n, a(n) for n = 0..1000</a>
%F 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
%F a(0) = 1, a(n) = -(7/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 05 2017
%F G.f.: exp(-7*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 06 2018
%t nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^7, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)
%o (PARI) x='x+O('x^50); Vec(prod(m=1, 50, (1 + x^m)^(-7))) \\ _Indranil Ghosh_, Apr 05 2017
%Y Column k=7 of A286352.
%K sign
%O 0,2
%A _N. J. A. Sloane_
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