A294978 Coefficients in expansion of (E_4/E_2^4)^(1/8).

1, 42, -2268, 395304, -64600914, 11644170552, -2188350306072, 424652412357696, -84326944950450972, 17044476557469661986, -3493525880987663047128, 724189608821718233434296, -151528575864988356484968840, 31955212589107172812017247992

Offset: 0

Author

Seiichi Manyama, Feb 12 2018

Keywords

• sign

Comments

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

Crossrefs

Cf. A004009 (E_4), A006352 (E_2), A108091, A289565, A294626, A294974.

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}];
(E4[x]/E2[x]^4)^(1/8) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

Convolution inverse of A294974.

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

a(n) ~ -(-1)^n * Pi^(5/4) * exp(Pi*sqrt(3)*n) / (2^(19/8) * 3^(9/8) * Gamma(2/3)^(9/4) * Gamma(7/8) * n^(9/8)). - Vaclav Kotesovec, Jun 03 2018