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A300055 Coefficients in expansion of (E_4^3/E_6^2)^(1/2).

%I A300055 #16 Mar 04 2018 11:42:21
%S A300055 1,864,476928,254399616,136313874432,72985679394624,39084426149704704,
%T A300055 20929208813297429760,11207444175842517172224,
%U A300055 6001488285356611750823136,3213747681163891383409648128,1720934927015053152217599326592
%N A300055 Coefficients in expansion of (E_4^3/E_6^2)^(1/2).
%H A300055 Seiichi Manyama, <a href="/A300055/b300055.txt">Table of n, a(n) for n = 0..366</a>
%F A300055 Convolution inverse of A299413.
%F A300055 a(n) ~ 16 * Pi^3 * exp(2*Pi*n) / (sqrt(3) * Gamma(1/4)^4). - _Vaclav Kotesovec_, Mar 04 2018
%t A300055 terms = 12;
%t A300055 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A300055 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A300055 (E4[x]^3/E6[x]^2)^(1/2) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 28 2018 *)
%Y A300055 (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), A300054 (k=96), this sequence (k=144), A289209 (k=288).
%Y A300055 Cf. A004009 (E_4), A013973 (E_6), A299413.
%K A300055 nonn
%O A300055 0,2
%A A300055 _Seiichi Manyama_, Feb 23 2018