A386816 Coefficients in q-expansion of E_2^2 * E_4^3, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.

1, 672, 145152, 8663424, -337036224, -6505531200, 40579467264, 1996981485312, 25931378854080, 210242562994464, 1273050737441280, 6245511315490944, 26057670474216192, 95466371280176064, 314217417062264832, 945050326572360960, 2631525623493208512, 6854684254893824832

Offset: 0

Author

Vaclav Kotesovec, Aug 03 2025

Keywords

• sign

Crossrefs

Cf. A006352, A004009, A386787.

Programs

Mathematica

terms = 20;
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}];
CoefficientList[Series[E2[x]^2*E4[x]^3, {x, 0, 20}], x]