A282208 Coefficients in q-expansion of E_2^2*E_4, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.

1, 192, -8928, 9984, 1420896, 11433600, 53760384, 187233792, 533725920, 1327018944, 2953851840, 6060858624, 11611915392, 21030301824, 36387585792, 60357358080, 97020376032, 150755202432, 229107724704, 338493223680, 492378465600, 698632525824, 980953593984

Offset: 0

Author

Seiichi Manyama, Feb 09 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A281374 (E_2^2), A282019 (E_2*E_4), A008410 (E_4^2 = E_8), A282018 (E_2^3), this sequence (E_2^2*E_4), A282101 (E_2*E_4^2), A008411 (E_4^3).

Programs

Mathematica

terms = 23;
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]^2*E4[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)