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%I #19 Mar 05 2018 09:31:53
%S 1,-168,-33768,-9806496,-3482370024,-1364023149552,-567278132268960,
%T -245678241438057792,-109559333350138970088,-49951945835561166375048,
%U -23173552482577051154061168,-10901813191731667585777068000
%N Coefficients in expansion of E_6^(1/3).
%H Seiichi Manyama, <a href="/A289327/b289327.txt">Table of n, a(n) for n = 0..367</a>
%F G.f.: Product_{n>=1} (1-q^n)^(A288851(n)/3).
%F a(n) ~ c * exp(2*Pi*n) / n^(4/3), where c = -3^(1/6) * Gamma(1/4)^(16/3) * Gamma(1/3) / (32 * 2^(1/3) * Pi^5) = -0.25096087408563316781920388861983614789... - _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}])^(1/3), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 08 2017 *)
%Y E_6^(k/12): A109817 (k=1), A289325 (k=2), A289326 (k=3), this sequence (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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