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%I #16 Mar 07 2018 09:54:44
%S 1,-5952,18352224,-39044962048,64418979107376,-87832074172772736,
%T 102995856743010218624,-106751551557580631373312,
%U 99750353173835532264248472,-85298079996944806752079602240,67533359025085585021484468850240,-49969584220872820552640845366351104,34818371808714662813628963122182100160
%N Expansion of 1/j^8 where j is the elliptic modular invariant (A000521).
%H Seiichi Manyama, <a href="/A289515/b289515.txt">Table of n, a(n) for n = 8..414</a>
%F a(n) ~ (-1)^n * 2^(3*k) * Pi^(12*k) * exp(Pi*sqrt(3)*n) * n^(3*k - 1) / (3^(3*k) * Gamma(1/3)^(18*k) * Gamma(3*k)), set k = 8. - _Vaclav Kotesovec_, Mar 07 2018
%t a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^8, {q, 0, n}]; Table[a[n], {n, 8, 20}] (* _Jean-François Alcover_, Nov 02 2017 *)
%Y Cf. A000521 (j).
%Y 1/j^k: A066395 (k=1), A288727 (k=2), A289454 (k=3), A289455 (k=4), A289512 (k=5), A289513 (k=6), A289514 (k=7), this sequence (k=8), A289516 (k=9), A289517 (k=10).
%K sign
%O 8,2
%A _Seiichi Manyama_, Jul 07 2017
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