A386815 Coefficients in q-expansion of E_2^4 * E_4^2, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.

1, 384, 19008, -3408384, 86384832, 390216960, -20773815552, -154767455232, 1360271378880, 30429758560128, 278226995437440, 1749537534970368, 8664534035259648, 36062711146189056, 131104383085776384, 427185615341306880, 1270776436150340544, 3499300888293305088, 9016032242401655616

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]^4*E4[x]^2, {x, 0, 20}], x]