A282330 Coefficients in q-expansion of E_4^6, where E_4 is the Eisenstein series A004009.

1, 1440, 876960, 292072320, 57349833120, 6660135541440, 436536302762880, 15172132360815360, 327295477379498400, 4913576699608450080, 55439481453769056960, 496426192564963006080, 3672749219557161663360, 23148323907214334109120

Offset: 0

Author

Seiichi Manyama, Feb 12 2017

Keywords

• nonn

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), A008410 (E_4^2), A008411 (E_4^3), A282012 (E_4^4), A282015 (E_4^5), this sequence (E_4^6).

Programs

Mathematica

terms = 14;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^6 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)

Formula

G.f.: (1 + 240 Sum_{i>=1} i^3 q^i/(1-q^i))^6.