A299698 Coefficients in expansion of (E_4^3/E_6^2)^(1/48).

1, 36, 4968, 2551824, 910405152, 416585268216, 182967944992992, 85373023607994528, 40055910812083687680, 19194979975339075406388, 9284600439037161721276848, 4539375955473797523355108272, 2236041702620444573315950439808

Offset

0,2

Links

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

Formula

Convolution inverse of A297021.

a(n) ~ 2^(1/6) * Pi^(1/8) * exp(2*Pi*n) / (3^(1/48) * Gamma(1/24) * Gamma(1/4)^(1/6) * n^(23/24)). - Vaclav Kotesovec, Mar 04 2018

a(n) * A297021(n) ~ -sin(Pi/24) * exp(4*Pi*n) / (24*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)^(1/48) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Crossrefs

(E_4^3/E_6^2)^(k/288): A289365 (k=1), A299694 (k=2), A299696 (k=3), A299697 (k=4), this sequence (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), A297021.

Sequence in context: A127860 A189148 A270506 * A203752 A184135 A275050

Adjacent sequences: A299695 A299696 A299697 * A299699 A299700 A299701

Keyword

nonn

Author

Seiichi Manyama, Feb 16 2018

Status

approved