A386817 Coefficients in q-expansion of E_2^3 * E_4 * E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.

1, -336, -114912, 4151616, 100931712, -2848456800, -37865826432, 222362076288, 7928555745600, 86986313152368, 620751040620480, 3392046804500928, 15293330001535488, 59435665658243616, 204976008706800384, 640351567531186560, 1840291945275505344, 4923361835292283488

Offset: 0

Author

Vaclav Kotesovec, Aug 03 2025

Keywords

• sign

Crossrefs

Cf. A006352, A004009, A013973, 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}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
CoefficientList[Series[E2[x]^3*E4[x]*E6[x], {x, 0, 20}], x]