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

0,2

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

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.

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 *)

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.

Sequence in context: A022056 A107520 A268877 * A367735 A217656 A020390

Adjacent sequences: A282012 A282013 A282014 * A282016 A282017 A282018

Keyword

nonn

Author

Seiichi Manyama, Feb 05 2017

Status

approved