A282328 Coefficients in q-expansion of E_4*E_6^3, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

1, -1272, 351432, 89559456, -28689603384, -3415837464144, -155926897275744, -3967939206760128, -65540990858009400, -777517458842153496, -7105797244669716432, -52584588767807410464, -326903749149928526688, -1755591468945924647184

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. A004009 (E_4), A013973 (E_6).

Cf. A013974 (E_4*E_6 = E_10), A282287 (E_4*E_6^2), this sequence (E_4*E_6^3).

Programs

Mathematica

terms = 14;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E4[x]*E6[x]^3 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)