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%I #38 Mar 05 2018 07:45:15
%S 1,-1488,1266840,-811420480,434731407660,-205762405603104,
%T 88869953694086720,-35768448018942261120,13610297613250180785870,
%U -4947238483283026511913200,1731166476103096494953112096,-586625688530872572480200739648
%N Expansion of 1/j^2 where j is the elliptic modular invariant (A000521).
%H Seiichi Manyama, <a href="/A288727/b288727.txt">Table of n, a(n) for n = 2..420</a>
%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) * n^5, where c = 8 * Pi^24 / (5 * 3^7 * Gamma(1/3)^36) = 0.000000245024306665040229500554761856570608172017999096... - _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)^2, {x, 0, nmax}], x], 2] (* _Vaclav Kotesovec_, Jul 07 2017 *)
%t a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^2, {q, 0, n}]; Table[a[n], {n, 2, 13}] (* _Jean-François Alcover_, Nov 02 2017 *)
%Y Cf. A000521 (j).
%Y 1/j^k: A066395 (k=1), this sequence (k=2), A289454 (k=3), A289455 (k=4).
%K sign
%O 2,2
%A _Seiichi Manyama_, Jul 06 2017
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