A299953 - OEIS

%I #18 Mar 04 2018 12:36:14

%S 1,144,27648,12540096,4971036672,2263040955360,1031452724072448,

%T 487587831652591488,233267529030162186240,113311495859272029716688,

%U 55566291037565862262794240,27487705978359515260636550208,13689979692617556597746930024448

%N Coefficients in expansion of (E_4^3/E_6^2)^(1/12).

%H Seiichi Manyama, <a href="/A299953/b299953.txt">Table of n, a(n) for n = 0..367</a>

%F Convolution inverse of A299858.

%F a(n) ~ 2^(2/3) * sqrt(Pi) * exp(2*Pi*n) / (3^(1/12) * Gamma(1/6) * Gamma(1/4)^(2/3) * n^(5/6)). - _Vaclav Kotesovec_, Mar 04 2018

%F a(n) * A299858(n) ~ -exp(4*Pi*n) / (12*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)^(1/12) + 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), A299943 (k=8), A299949 (k=9), A289369 (k=12), A299950 (k=16), A299951 (k=18), this sequence (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), A299858.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 22 2018