|
%I #18 Mar 04 2018 12:33:37
%S 1,24,3168,1663776,584685312,268219092816,117214929608832,
%T 54637244971358016,25574598700199847936,12238100148358426410360,
%U 5910293921259795914011968,2885917219371433467109558368,1419817980186833008095972357120
%N Coefficients in expansion of (E_4^3/E_6^2)^(1/72).
%H Seiichi Manyama, <a href="/A299697/b299697.txt">Table of n, a(n) for n = 0..367</a>
%F Convolution inverse of A296652.
%F a(n) ~ 2^(1/9) * Pi^(1/12) * exp(2*Pi*n) / (3^(1/72) * Gamma(1/36) * Gamma(1/4)^(1/9) * n^(35/36)). - _Vaclav Kotesovec_, Mar 04 2018
%F a(n) * A296652(n) ~ -sin(Pi/36) * exp(4*Pi*n) / (36*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)^(1/72) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y (E_4^3/E_6^2)^(k/288): A289365 (k=1), A299694 (k=2), A299696 (k=3), this sequence (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 Cf. A004009 (E_4), A013973 (E_6), A296652.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 16 2018
|
