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%I #12 Apr 05 2017 09:51:11
%S 1,-19,171,-988,4237,-14896,46075,-130549,344888,-858325,2032924,
%T -4621313,10137716,-21545639,44525987,-89757843,176925625,-341688495,
%U 647687314,-1206921212,2213842874,-4001882220,7136374179
%N Expansion of Product_{m>=1} (1+q^m)^(-19).
%H Seiichi Manyama, <a href="/A022614/b022614.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ (-1)^n * 19^(1/4) * exp(Pi*sqrt(19*n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 27 2015
%F a(0) = 1, a(n) = -(19/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 05 2017
%t nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^19, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)
%K sign
%O 0,2
%A _N. J. A. Sloane_
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