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A299696 Coefficients in expansion of (E_4^3/E_6^2)^(1/96).

%I A299696 #17 Mar 04 2018 12:33:10
%S A299696 1,18,2322,1234116,430292646,197681749128,86165040337452,
%T A299696 40145493017336976,18768723217958523222,8975036477140737601806,
%U A299696 4331009172188712335053032,2113419430011730408087143924,1039122180212218474089489166980
%N A299696 Coefficients in expansion of (E_4^3/E_6^2)^(1/96).
%H A299696 Seiichi Manyama, <a href="/A299696/b299696.txt">Table of n, a(n) for n = 0..368</a>
%F A299696 Convolution inverse of A296614.
%F A299696 a(n) ~ 2^(1/12) * Pi^(1/16) * exp(2*Pi*n) / (3^(1/96) * Gamma(1/48) * Gamma(1/4)^(1/12) * n^(47/48)). - _Vaclav Kotesovec_, Mar 04 2018
%F A299696 a(n) * A296614(n) ~ -sin(Pi/48) * exp(4*Pi*n) / (48*Pi*n^2). - _Vaclav Kotesovec_, Mar 04 2018
%t A299696 terms = 13;
%t A299696 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A299696 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A299696 (E4[x]^3/E6[x]^2)^(1/96) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y A299696 (E_4^3/E_6^2)^(k/288): A289365 (k=1), A299694 (k=2), this sequence (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), A300055 (k=144), A289209 (k=288).
%Y A299696 Cf. A004009 (E_4), A013973 (E_6), A296614.
%K A299696 nonn
%O A299696 0,2
%A A299696 _Seiichi Manyama_, Feb 16 2018