A299694 - OEIS

%I #22 Mar 04 2018 12:32:40

%S 1,12,1512,813744,281434656,129501949608,56296822560480,

%T 26218237904433888,12242575532254540032,5850239653863742634172,

%U 2820869122426120317439152,1375631026432164061822527120,675950202173640832786529615232

%N Coefficients in expansion of (E_4^3/E_6^2)^(1/144).

%H Seiichi Manyama, <a href="/A299694/b299694.txt">Table of n, a(n) for n = 0..368</a>

%F Convolution inverse of A296609.

%F a(n) ~ 2^(1/18) * Pi^(1/24) * exp(2*Pi*n) / (3^(1/144) * Gamma(1/72) * Gamma(1/4)^(1/18) * n^(71/72)). - _Vaclav Kotesovec_, Mar 04 2018

%F a(n) * A296609(n) ~ -sin(Pi/72) * exp(4*Pi*n) / (72*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)^(1/144) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y (E_4^3/E_6^2)^(k/288): A289365 (k=1), this sequence (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), A300055 (k=144), A289209 (k=288).

%Y Cf. A004009 (E_4), A013973 (E_6), A296609.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 16 2018