A282047 Coefficients in q-expansion of E_4^4*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

1, 456, -146232, -133082976, -32170154808, -3378441902544, -155862776255328, -3969266446940352, -65538944782146360, -777506848190979672, -7105808014591457232, -52584752452485047328, -326903300701760852832, -1755591608260377411216

Offset

0,2

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

Formula

-552 * A013969(n) = 77683 * a(n) - 35424000 * A037946(n) for n > 0.

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]^4*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

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), this sequence (E_4^4*E_6), A282048 (E_4^5*E_6).

Cf. A013969, A037946, A281956.

Sequence in context: A282101 A037945 A278731 * A278433 A278551 A278796

Adjacent sequences: A282044 A282045 A282046 * A282048 A282049 A282050

Keyword

sign

Author

Seiichi Manyama, Feb 05 2017

Status

approved