A282331 Coefficients in q-expansion of E_6^4, where E_6 is the Eisenstein series A013973.

1, -2016, 1457568, -411997824, 16227967392, 6497071680960, 440015323483008, 15172068869975808, 327221898778968480, 4913597307075535008, 55440561879404210880, 496424806634688962688, 3672744471642078903168, 23148319448757751932096

Offset: 0

Author

Seiichi Manyama, Feb 12 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Eisenstein Series.

Crossrefs

Cf. A013973 (E_6), A280869 (E_6^2), A282253 (E_6^3), this sequence (E_6^4).

Cf. A282210 (E_2^4), A282012 (E_4^4), this sequence (E_6^4).

Programs

Mathematica

terms = 14;
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E6[x]^4 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)

Formula

E6(q)^4 = (1 - 504 Sum_{i>=1} sigma_5(i)q^i)^4 where sigma_5(n) is A001160.