A282012 Coefficients in q-expansion of E_4^4, where E_4 is the Eisenstein series shown in A004009.

1, 960, 354240, 61543680, 4858169280, 137745912960, 2120861041920, 21423820362240, 158753769048000, 928983317334720, 4512174992346240, 18847874280625920, 69518972236842240, 230951926208599680, 701949379778818560, 1975788826748167680

Offset: 0

Author

Seiichi Manyama, Feb 04 2017

Keywords

• nonn

Comments

Also coefficients in q-expansion of E_8^2.

References

• G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 207.

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), this sequence (E_4^4), A282015 (E_4^5).

Cf. A281374 (E_2^2), A008410 (E_4^2), A280869 (E_6^2), this sequence (E_8^2), A282292 (E_10^2).

Cf. A013963, A027364, A281876.

Programs

Mathematica

terms = 16;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^4 + 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))^4.

16320 * A013963(n) = 3617 * a(n) - 3456000 * A027364(n) for n > 0.