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%I #23 Mar 05 2018 09:31:19
%S 1,-126,-27972,-8603784,-3156774138,-1265670056952,-536028623834760,
%T -235629947944839168,-106414175763732002292,-49052892961209924090486,
%U -22977990271885179647877768,-10904016663130642099838196120
%N Coefficients in expansion of E_6^(1/4).
%H Seiichi Manyama, <a href="/A289326/b289326.txt">Table of n, a(n) for n = 0..367</a>
%F G.f.: Product_{n>=1} (1-q^n)^(A288851(n)/4).
%F a(n) ~ c * exp(2*Pi*n) / n^(5/4), where c = -sqrt(3) * Gamma(1/4)^5 / (32 * 2^(3/4) * Pi^4) = -0.20698746071805886655919194203910626895689130674662074751291... - _Vaclav Kotesovec_, Jul 08 2017, updated Mar 05 2018
%t nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(1/4), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 08 2017 *)
%Y E_6^(k/12): A109817 (k=1), A289325 (k=2), this sequence (k=3), A289327 (k=4), A289328 (k=5), A289293 (k=6), A289345 (k=7), A289346 (k=8), A289347 (k=9), A289348 (k=10), A289349 (k=11).
%Y Cf. A013973 (E_6), A288851.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jul 02 2017
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