A282102 Coefficients in q-expansion of E_2*E_4*E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.

1, -288, -129168, -1927296, 65152656, 1535768640, 15223408704, 98001292032, 474055120080, 1870878793824, 6312358836000, 18835985199744, 50831420617152, 126257508465984, 292348744636032, 637474437331200, 1319883180896592, 2610964045674432, 4963491913583664

Offset: 0

Author

Seiichi Manyama, Feb 06 2017

Keywords

• sign

Comments

The series expansion of the 12th root of the generating function gives A341801. - Peter Bala, Feb 23 2021

Links

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

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A013974 (E_10).

Cf. A281374 (E_2^2), A282019 (E_2*E_4), A282096 (E_2*E_6), A282101 (E_2*E_8), this sequence (E_2*E_10), A341801.

Programs

Mathematica

terms = 19;
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}];
E2[x]*E4[x]*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)