A037164 Numerators of coefficients of Eisenstein series E_12(q) (or E_6(q) or E_24(q)).

1, 65520, 134250480, 11606736960, 274945048560, 3199218815520, 23782204031040, 129554448266880, 563087459516400, 2056098632318640, 6555199353000480, 18693620658498240, 48705965462306880, 117422349017369760, 265457064498837120, 566735214731736960, 1153203117089652720

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Comments

First denominator is 1, rest are 691.

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.
• J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.

Links

• Andy Huchala, Table of n, a(n) for n = 0..20000
• H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
• Index entries for sequences related to Eisenstein series

Crossrefs

Cf. A029828.

Programs

Maple

with(numtheory):
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(12);
seq(numer(coeff(%,q,n)), n=0..24);

Mathematica

terms = 13; E12[x_] = 1 - (24/BernoulliB[12])*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}]; E12[x] + O[x]^terms // CoefficientList[#, x]& // Numerator (* Jean-François Alcover, Feb 27 2018 *)

Sage

l = list(eisenstein_series_qexp(12,20, normalization='integral'))
l[0] = 1; l # Andy Huchala, Jul 01 2021