A282000 Coefficients in q-expansion of E_4^3*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

1, 216, -200232, -85500576, -11218984488, -499862636784, -11084671590048, -152346382155072, -1474691273530920, -10921720940625672, -65489246355989232, -331011680696545248, -1452954445366288032, -5665058572086302256, -19968589327695656256

Offset: 0

Author

Seiichi Manyama, Feb 05 2017

Keywords

• sign

References

• G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.

Links

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

Crossrefs

Cf. A004009 (E_4), A013973 (E_6), A013974 (E_4*E_6 = E_10), A058550 (E_4^2*E_6 = E_14), this sequence (E_4^3*E_6), A282047 (E_4^4*E_6), A282048 (E_4^5*E_6).

Cf. A013965, A037944, A281928.

Programs

Mathematica

terms = 15;
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]^3*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

-28728 * A013965(n) = 43867 * a(n) - 9504000 * A037944(n) for n > 0.