%I #17 Mar 04 2018 12:38:03
%S 1,576,235008,109880064,53449592832,26574124961664,13393739222599680,
%T 6814262482916285952,3490692930294883909632,1797524713443792341369664,
%U 929454499859725260939506688,482202319224911188610453541120
%N Coefficients in expansion of (E_4^3/E_6^2)^(1/3).
%H Seiichi Manyama, <a href="/A300054/b300054.txt">Table of n, a(n) for n = 0..366</a>
%F Convolution inverse of A299414.
%F a(n) ~ 2^(8/3) * Pi^2 * exp(2*Pi*n) / (3^(1/3) * Gamma(1/4)^(8/3) * Gamma(2/3) * n^(1/3)). - _Vaclav Kotesovec_, Mar 04 2018
%F a(n) * A299414(n) ~ -exp(4*Pi*n) / (sqrt(3)*Pi*n^2). - _Vaclav Kotesovec_, Mar 04 2018
%t terms = 12;
%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t (E4[x]^3/E6[x]^2)^(1/3) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 28 2018 *)
%Y (E_4^3/E_6^2)^(k/288): A289365 (k=1), A299694 (k=2), A299696 (k=3), A299697 (k=4), A299698 (k=6), A299943 (k=8), A299949 (k=9), A289369 (k=12), A299950 (k=16), A299951 (k=18), A299953 (k=24), A299993 (k=32), A299994 (k=36), A300052 (k=48), A300053 (k=72), this sequence (k=96), A300055 (k=144), A289209 (k=288).
%Y Cf. A004009 (E_4), A013973 (E_6), A299414.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 23 2018
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