A294974 Coefficients in expansion of (E_2^4/E_4)^(1/8).

1, -42, 4032, -659904, 118064226, -22406634432, 4407587356032, -888750999070464, 182478248639753472, -37986867560948245674, 7994272624037726124672, -1697243410477799687716416, 362963150140702802158191360, -78095916585903527021840348352

Offset: 0

Author

Seiichi Manyama, Feb 12 2018

Keywords

• sign

Comments

Also coefficients in expansion of (E_2^8/E_8)^(1/16).

Crossrefs

Cf. A004009 (E_4), A006352 (E_2), A108091, A289247, A289291, A294626, A294976.

Programs

Mathematica

terms = 14;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
(E2[x]^4/E4[x])^(1/8) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^A294626(n).

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