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

0,2

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

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

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 *)

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.

Sequence in context: A048100 A222337 A008697 * A013785 A100509 A378265

Adjacent sequences: A281997 A281998 A281999 * A282001 A282002 A282003

Keyword

sign

Author

Seiichi Manyama, Feb 05 2017

Status

approved