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

0,2

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

Table of n, a(n) for n=0..12.

Index entries for sequences related to Eisenstein series

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 *)

Crossrefs

Cf. A029829.

Sequence in context: A043607 A067375 A237460 * A337417 A013690 A247826

Adjacent sequences: A058549 A058550 A058551 * A058553 A058554 A058555

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 25 2000

Status

approved