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A299859 Coefficients in expansion of (E_6^2/E_4^3)^(1/8).

%I A299859 #17 Mar 04 2018 12:44:13
%S A299859 1,-216,-2592,-10412064,-1955812608,-1193816824272,-424976182312320,
%T A299859 -205525905843878208,-89308328381644142592,-42098146869799454214456,
%U A299859 -19580168925118916335723968,-9345687920591466548039096160
%N A299859 Coefficients in expansion of (E_6^2/E_4^3)^(1/8).
%H A299859 Seiichi Manyama, <a href="/A299859/b299859.txt">Table of n, a(n) for n = 0..367</a>
%F A299859 G.f.: (1 - 1728/j)^(1/8), where j is the j-function.
%F A299859 a(n) ~ -3^(1/8) * Gamma(1/4) * exp(2*Pi*n) / (8 * Pi^(3/4) * Gamma(3/4) * n^(5/4)). - _Vaclav Kotesovec_, Mar 04 2018
%F A299859 a(n) * A299994(n) ~ -exp(4*Pi*n) / (4*sqrt(2)*Pi*n^2). - _Vaclav Kotesovec_, Mar 04 2018
%t A299859 terms = 12;
%t A299859 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A299859 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A299859 (E6[x]^2/E4[x]^3)^(1/8) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 28 2018 *)
%Y A299859 (E_6^2/E_4^3)^(k/288): A289366 (k=1), A296609 (k=2), A296614 (k=3), A296652 (k=4), A297021 (k=6), A299422 (k=8), A299862 (k=9), A289368 (k=12), A299856 (k=16), A299857 (k=18), A299858 (k=24), A299863 (k=32), this sequence (k=36), A299860 (k=48), A299861 (k=72), A299414 (k=96), A299413 (k=144), A289210 (k=288).
%Y A299859 Cf. A000521 (j).
%K A299859 sign
%O A299859 0,2
%A A299859 _Seiichi Manyama_, Feb 21 2018