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A299858 Coefficients in expansion of (E_6^2/E_4^3)^(1/12).

%I A299858 #17 Mar 04 2018 12:43:32
%S A299858 1,-144,-6912,-7563456,-1885022208,-979976901600,-383134788854784,
%T A299858 -179914112738674560,-80649007527361757184,-38019764211792500474064,
%U A299858 -17921855069499640580651520,-8604055343353988623666807872
%N A299858 Coefficients in expansion of (E_6^2/E_4^3)^(1/12).
%H A299858 Seiichi Manyama, <a href="/A299858/b299858.txt">Table of n, a(n) for n = 0..367</a>
%F A299858 G.f.: (1 - 1728/j)^(1/12), where j is the j-function.
%F A299858 a(n) ~ -Gamma(1/4)^(2/3) * exp(2*Pi*n) / (2^(5/3) * 3^(11/12) * sqrt(Pi) * Gamma(5/6) * n^(7/6)). - _Vaclav Kotesovec_, Mar 04 2018
%F A299858 a(n) * A299953(n) ~ -exp(4*Pi*n) / (12*Pi*n^2). - _Vaclav Kotesovec_, Mar 04 2018
%t A299858 terms = 12;
%t A299858 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A299858 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A299858 (E6[x]^2/E4[x]^3)^(1/12) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 28 2018 *)
%Y A299858 (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), this sequence (k=24), A299863 (k=32), A299859 (k=36), A299860 (k=48), A299861 (k=72), A299414 (k=96), A299413 (k=144), A289210 (k=288).
%Y A299858 Cf. A000521 (j).
%K A299858 sign
%O A299858 0,2
%A A299858 _Seiichi Manyama_, Feb 21 2018