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%I #21 Mar 28 2018 03:58:37
%S 1,-4,2,0,23,-20,2,-88,63,-96,318,-104,626,-844,504,-2472,1525,-3704,
%T 6184,-4288,15284,-10736,23254,-35792,30228,-84544,60974,-139240,
%U 176658,-190108,418940,-320976,755332,-773524,1111678,-1847304,1669046,-3634296
%N Expansion of Product_{k>0} 1/(1 + x^k)^(k*4).
%H Seiichi Manyama, <a href="/A279411/b279411.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ (-1)^n * exp(-1/3 + 3/2 * Zeta(3)^(1/3) * n^(2/3)) * A^4 * Zeta(3)^(1/18) / (sqrt(6*Pi) * n^(5/9)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Apr 13 2017
%F G.f.: exp(4*Sum_{k>=1} (-1)^k*x^k/(k*(1 - x^k)^2)). - _Ilya Gutkovskiy_, Mar 27 2018
%Y Column k=4 of A279928.
%Y Product_{k>0} 1/(1 + x^k)^(k*m): A027906 (m=-4), A255528 (m=1), A278710 (m=2), A279031 (m=3), this sequence (m=4), A279932 (m=5).
%K sign
%O 0,2
%A _Seiichi Manyama_, Apr 11 2017