A282792 Coefficients in q-expansion of E_2^2*E_4*E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.

1, -312, -122328, 1193376, 120735336, 123318576, -26119268064, -383848045248, -3132125965080, -18290795499096, -84925855577232, -331983655889184, -1133781877844448, -3470165144567184, -9697162366507968, -25093220330304576, -60786860467926552

Offset: 0

Author

Seiichi Manyama, Feb 21 2017

Keywords

• sign

Links

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

Crossrefs

Cf. A282102 (E_2*E_4*E_6), this sequence (E_2^2*E_4*E_6), A282596 (E_2*E_4^2*E_6), A282547 (E_2*E_4*E_6^2).

Programs

Mathematica

terms = 17;
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}];
E4[x]^2*E6[x]*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)