A282547 Coefficients in q-expansion of E_2*E_4*E_6^2, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.

1, -792, -648, 67840416, 3219716376, 16790031216, -1536150710304, -39898324202688, -522122582192040, -4650999065751096, -31648313780323632, -175516685804469024, -827282698744164768, -3413275186936731984, -12598131165680789568, -42296014044574387776

Offset: 0

Author

Seiichi Manyama, Feb 18 2017

Keywords

• sign

Links

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

Crossrefs

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

Programs

Mathematica

terms = 16;
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]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)