A294979 Coefficients in expansion of (E_2^6/E_6)^(1/12).

1, 30, 12240, 4620000, 1915684770, 839549366208, 381374756189280, 177631327935911040, 84272487587664762240, 40549569894460426101150, 19730577674798681251391712, 9687875889040210133058857760, 4792614349874614536514510456320

Offset: 0

Author

Seiichi Manyama, Feb 12 2018

Keywords

• nonn

Crossrefs

Cf. A289291, A289540, A294975, A294976.

Programs

Mathematica

terms = 13;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
(E2[x]^6/E6[x])^(1/12) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

Convolution inverse of A294976.

G.f.: Product_{n>=1} (1-q^n)^(-A294975(n)).

a(n) ~ 2^(13/12) * 3^(1/3) * sqrt(Pi) * exp(2*Pi*n) / (Gamma(1/12) * Gamma(1/4)^(4/3) * n^(11/12)). - Vaclav Kotesovec, Jun 03 2018