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

0,2

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

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 *)

Prog

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

Crossrefs

Cf. A029828.

Sequence in context: A083608 A102277 A013692 * A288990 A075964 A075969

Adjacent sequences: A037161 A037162 A037163 * A037165 A037166 A037167

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved