%I #18 Jun 03 2018 07:41:21
%S 1,30,12240,4620000,1915684770,839549366208,381374756189280,
%T 177631327935911040,84272487587664762240,40549569894460426101150,
%U 19730577674798681251391712,9687875889040210133058857760,4792614349874614536514510456320
%N Coefficients in expansion of (E_2^6/E_6)^(1/12).
%F Convolution inverse of A294976.
%F G.f.: Product_{n>=1} (1-q^n)^(-A294975(n)).
%F 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
%t terms = 13;
%t E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t (E2[x]^6/E6[x])^(1/12) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y Cf. A289291, A289540, A294975, A294976.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 12 2018