A299694 Coefficients in expansion of (E_4^3/E_6^2)^(1/144).

1, 12, 1512, 813744, 281434656, 129501949608, 56296822560480, 26218237904433888, 12242575532254540032, 5850239653863742634172, 2820869122426120317439152, 1375631026432164061822527120, 675950202173640832786529615232

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..368

Formula

Convolution inverse of A296609.

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

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

Crossrefs

(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).

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

Sequence in context: A276905 A015096 A271434 * A366832 A160237 A013474

Adjacent sequences: A299691 A299692 A299693 * A299695 A299696 A299697

Keyword

nonn

Author

Seiichi Manyama, Feb 16 2018

Status

approved