%I #16 Mar 07 2018 09:55:02
%S 1,-3720,7318620,-10127095360,11061866004390,-10151440298355744,
%T 8136148305855926840,-5846643254165797186560,
%U 3838606195380374717418465,-2335284727373310897029544400,1330851094413644423959537571652,-716606026961666494353690542814720
%N Expansion of 1/j^5 where j is the elliptic modular invariant (A000521).
%H Seiichi Manyama, <a href="/A289512/b289512.txt">Table of n, a(n) for n = 5..417</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 = 5. - _Vaclav Kotesovec_, Mar 07 2018
%t a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^5, {q, 0, n}]; Table[a[n], {n, 5, 16}] (* _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), this sequence (k=5), A289513 (k=6), A289514 (k=7), A289515 (k=8), A289516 (k=9), A289517 (k=10).
%K sign
%O 5,2
%A _Seiichi Manyama_, Jul 07 2017