A294182 Coefficients in expansion of E_4/E_6.

1, 744, 393768, 210962976, 112966533672, 60492691156464, 32393330061359904, 17346357971979746880, 9288829947058862457384, 4974090926254339741926216, 2663584184830281769743846768, 1426327104764356980195826984032

Offset: 0

Author

Seiichi Manyama, Feb 11 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A000706, A004009 (E_4), A013973 (E_6), A288261.

E_k/E_{k+2}: A294181 (k=2), this sequence (k=4), A294183 (k=6).

Programs

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]/E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)

Formula

Convolution inverse of A288261.

a(n) ~ 8 * Gamma(3/4)^8 * exp(2*Pi*n) / (3*Pi^2). - Vaclav Kotesovec, Jun 03 2018