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%I #17 Mar 05 2018 04:34:07
%S 1,150,-5400,625200,-86672550,13570016400,-2289741037200,
%T 406440122001600,-74830416797043000,14162747887897808550,
%U -2738995393669565720400,538973037306449327998800,-107578899914865970323788400,21729813219122500082762389200
%N Coefficients in expansion of E_4^(5/8).
%H Seiichi Manyama, <a href="/A289309/b289309.txt">Table of n, a(n) for n = 0..425</a>
%F G.f.: Product_{n>=1} (1-q^n)^(5*A110163(n)/8).
%F a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(13/8), where c = 5 * 3^(5/4) * Gamma(1/3)^(45/4) / (256 * 2^(5/8) * Pi^(15/2) * Gamma(3/8)) = 0.2571085249207580781634342667473393997795373224370302803101380883544... - _Vaclav Kotesovec_, Jul 08 2017, updated Mar 05 2018
%t nmax = 20; CoefficientList[Series[(1 + 240*Sum[DivisorSigma[3,k]*x^k, {k, 1, nmax}])^(5/8), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 08 2017 *)
%Y E_4^(k/8): A108091 (k=1), A289307 (k=2), A289308 (k=3), A289292 (k=4), this sequence (k=5), A289318 (k=6), A289319 (k=7).
%Y Cf. A004009 (E_4), A110163.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jul 02 2017
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