A282048 Coefficients in q-expansion of E_4^5*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

1, 696, -34632, -167186976, -64422848328, -11387712944304, -1037073232984608, -48892286706157632, -1378097272692189000, -26188038166214133672, -364779879415169299632, -3952277018332870144608, -34798618196377082329632, -257403706082325167732976

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), A282000 (E_4^3*E_6), A282047 (E_4^4*E_6), this sequence (E_4^5*E_6).

Cf. A037947, A281959, A281979.

Programs

Mathematica

terms = 14;
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]^5*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)

Formula

-24 * A281959(n) = 657931 * a(n) - 457920000 * A037947(n) for n > 0.