A282015 Coefficients in q-expansion of E_4^5, where E_4 is the Eisenstein series shown in A004009.

1, 1200, 586800, 148641600, 20400279600, 1439038231200, 46093334702400, 861697555612800, 10894180752126000, 102121497049868400, 755966260027216800, 4623420005167550400, 24151632380348692800, 110516281318431693600, 451789183426135939200

Offset: 0

Author

Seiichi Manyama, Feb 05 2017

Keywords

• nonn

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), A008410 (E_4^2), A008411 (E_4^3), A282012 (E_4^4), this sequence (E_4^5).

Cf. A013967, A037945, A281788.

Programs

Mathematica

terms = 15;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^5 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

G.f.: (1 + 240 Sum_{i>=1} i^3 q^i/(1-q^i))^5.

13200 * A013967(n) = 174611 * a(n) - 209520000 * A037945(n) for n > 0.