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A299951 Coefficients in expansion of (E_4^3/E_6^2)^(1/16).

%I A299951 #19 Mar 04 2018 12:35:51
%S A299951 1,108,18792,8775216,3375768096,1535055129576,691959629136096,
%T A299951 325485731190285792,154751723387164258560,74822912718767823810204,
%U A299951 36526619326785857845042608,17998154668247683887778684176,8931078840823632559970453020032
%N A299951 Coefficients in expansion of (E_4^3/E_6^2)^(1/16).
%H A299951 Seiichi Manyama, <a href="/A299951/b299951.txt">Table of n, a(n) for n = 0..367</a>
%F A299951 Convolution inverse of A299857.
%F A299951 a(n) ~ sqrt(2) * Pi^(3/8) * exp(2*Pi*n) / (3^(1/16) * Gamma(1/8) * sqrt(Gamma(1/4)) * n^(7/8)). - _Vaclav Kotesovec_, Mar 04 2018
%F A299951 a(n) * A299857(n) ~ -sin(Pi/8) * exp(4*Pi*n) / (8*Pi*n^2). - _Vaclav Kotesovec_, Mar 04 2018
%t A299951 terms = 13;
%t A299951 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A299951 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A299951 (E4[x]^3/E6[x]^2)^(1/16) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 28 2018 *)
%Y A299951 (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), this sequence (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 A299951 Cf. A004009 (E_4), A013973 (E_6), A299857.
%K A299951 nonn
%O A299951 0,2
%A A299951 _Seiichi Manyama_, Feb 22 2018