A299950 Coefficients in expansion of (E_4^3/E_6^2)^(1/18).

1, 96, 16128, 7622784, 2900355072, 1319081479488, 592274331915264, 278167185566287104, 131973896384325992448, 63712327450686749464032, 31055582715009234813891072, 15282363171869402875165461888, 7574187854327285047920802652160

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..367

Formula

Convolution inverse of A299856.

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

a(n) * A299856(n) ~ -sin(Pi/9) * exp(4*Pi*n) / (9*Pi*n^2). - Vaclav Kotesovec, Mar 04 2018

Mathematica

terms = 13;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
(E4[x]^3/E6[x]^2)^(1/18) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 28 2018 *)

Crossrefs

(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).

Cf. A004009 (E_4), A013973 (E_6), A299856.

Sequence in context: A216039 A208443 A183418 * A269208 A295597 A203489

Adjacent sequences: A299947 A299948 A299949 * A299951 A299952 A299953

Keyword

nonn

Author

Seiichi Manyama, Feb 22 2018

Status

approved