A058552 Numerators of q-expansion of Eisenstein series E_16(q).

1, 16320, 534790080, 234174178560, 17524001357760, 498046875016320, 7673653657232640, 77480203842286080, 574226476491096000, 3360143509958850240, 16320498047409790080, 68172690124863440640, 251450283274373326080

Offset: 0

Author

N. J. A. Sloane, Dec 25 2000

Keywords

• nonn
• frac

Comments

Denominators are 3617 except for leading term for which denominator is 1.

References

• R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 53.
• N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 1984, see p. 111.

Links

• Index entries for sequences related to Eisenstein series

Crossrefs

Cf. A029829.

Programs

Maple

E := proc(k) local n,t1; t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n,n=1..60); series(t1,q,60); end; E(16);

Mathematica

terms = 13; E16[x_] = 1 - (32/BernoulliB[16])*Sum[k^15*(x^k/(1 - x^k)), {k, 1, terms}]; E16[x] + O[x]^terms // CoefficientList[#, x]& // Numerator (* Jean-François Alcover, Feb 27 2018 *)