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%I #24 Mar 05 2018 07:56:59
%S 1,-2976,4747824,-5392956800,4889133749400,-3761165322168768,
%T 2549962294786430144,-1562849905009064897280,881746577453401952409900,
%U -464149085470990004575901600,230323243751761513144853469408,-108618796884881830752241855604352
%N Expansion of 1/j^4 where j is the elliptic modular invariant (A000521).
%H Seiichi Manyama, <a href="/A289455/b289455.txt">Table of n, a(n) for n = 4..418</a>
%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) * n^11, where c = 16 * Pi^48 / (82864937925 * Gamma(1/3)^72) = 0.00000000000000002165833724988588666420880993216216369751685... - _Vaclav Kotesovec_, Jul 07 2017, updated Mar 05 2018
%t nmax = 20; Drop[CoefficientList[Series[((1 - (1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}])^2/(1 + 240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])^3)/1728)^4, {x, 0, nmax}], x], 4] (* _Vaclav Kotesovec_, Jul 07 2017 *)
%t a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^4, {q, 0, n}]; Table[a[n], {n, 4, 15}] (* _Jean-François Alcover_, Nov 02 2017 *)
%Y Cf. A000521 (j).
%Y 1/j^k: A066395 (k=1), A288727 (k=2), A289454 (k=3), this sequence (k=4).
%K sign
%O 4,2
%A _Seiichi Manyama_, Jul 06 2017
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