%I #18 Mar 04 2018 05:45:48
%S 1,48,6912,3479616,1259268096,575044765344,253777092387840,
%T 118545813515338368,55748828845833043968,26753648919849657887472,
%U 12960874757914028815661568,6344939709971525751086888640,3129285552537639403735326646272
%N Coefficients in expansion of (E_4^3/E_6^2)^(1/36).
%H Seiichi Manyama, <a href="/A299943/b299943.txt">Table of n, a(n) for n = 0..367</a>
%F Convolution inverse of A299422.
%F a(n) ~ c * exp(2*Pi*n) / n^(17/18), where c = 2^(2/9) * Pi^(1/6) / (3^(1/36) * Gamma(1/4)^(2/9) * Gamma(1/18)) = 0.0588537525900341685779220592527938... - _Vaclav Kotesovec_, Mar 04 2018
%F a(n) * A299422(n) ~ -sin(Pi/18) * exp(4*Pi*n) / (18*Pi*n^2). - _Vaclav Kotesovec_, Mar 04 2018
%t terms = 13;
%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)^(1/36) + 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), this sequence (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 Cf. A004009 (E_4), A013973 (E_6), A299422.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 22 2018
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