A299950 - OEIS

%I #17 Mar 04 2018 08:47:41

%S 1,96,16128,7622784,2900355072,1319081479488,592274331915264,

%T 278167185566287104,131973896384325992448,63712327450686749464032,

%U 31055582715009234813891072,15282363171869402875165461888,7574187854327285047920802652160

%N Coefficients in expansion of (E_4^3/E_6^2)^(1/18).

%H Seiichi Manyama, <a href="/A299950/b299950.txt">Table of n, a(n) for n = 0..367</a>

%F Convolution inverse of A299856.

%F a(n) ~ c * exp(2*Pi*n) / n^(8/9), where c = 2^(4/9) * Pi^(1/3) / (3^(1/18) * Gamma(1/4)^(4/9) * Gamma(1/9)) = 0.124111089715926449273529850774692739948955... - _Vaclav Kotesovec_, Mar 04 2018

%F a(n) * A299856(n) ~ -sin(Pi/9) * exp(4*Pi*n) / (9*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)^(1/18) + 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), this sequence (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), A299856.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 22 2018