A300053 Coefficients in expansion of (E_4^3/E_6^2)^(1/4).

1, 432, 145152, 64494144, 29760915456, 14274670230432, 6975951829890048, 3459591515857458816, 1733116511275051696128, 875135886353582630388336, 444632598699435462934282752, 227042568315636603738176892096

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..366

Formula

Convolution inverse of A299861.

a(n) ~ 4 * Pi * exp(2*Pi*n) / (3^(1/4) * Gamma(1/4)^2 * sqrt(n)). - Vaclav Kotesovec, Mar 04 2018

a(n) * A299861(n) ~ -exp(4*Pi*n) / (2*Pi*n^2). - Vaclav Kotesovec, Mar 04 2018

Mathematica

terms = 12;
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)^(1/4) + 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), A299950 (k=16), A299951 (k=18), A299953 (k=24), A299993 (k=32), A299994 (k=36), A300052 (k=48), this sequence (k=72), A300054 (k=96), A300055 (k=144), A289209 (k=288).

Cf. A004009 (E_4), A013973 (E_6), A299861.

Sequence in context: A269211 A269094 A269273 * A047804 A008691 A269881

Adjacent sequences: A300050 A300051 A300052 * A300054 A300055 A300056

Keyword

nonn

Author

Seiichi Manyama, Feb 23 2018

Status

approved