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%I #20 Jun 03 2018 09:00:07
%S 1,-42,4032,-659904,118064226,-22406634432,4407587356032,
%T -888750999070464,182478248639753472,-37986867560948245674,
%U 7994272624037726124672,-1697243410477799687716416,362963150140702802158191360,-78095916585903527021840348352
%N Coefficients in expansion of (E_2^4/E_4)^(1/8).
%C Also coefficients in expansion of (E_2^8/E_8)^(1/16).
%F G.f.: Product_{n>=1} (1-q^n)^A294626(n).
%F a(n) ~ (-1)^n * 2^(13/8) * Pi * exp(Pi*sqrt(3)*n) / (Gamma(1/8) * Gamma(1/3)^(9/4) * n^(7/8)). - _Vaclav Kotesovec_, Jun 03 2018
%t terms = 14;
%t E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t (E2[x]^4/E4[x])^(1/8) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y Cf. A004009 (E_4), A006352 (E_2), A108091, A289247, A289291, A294626, A294976.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 12 2018
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