A029828 Eisenstein series E_12(q) (alternate convention E_6(q)), multiplied by 691.

691, 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

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

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to Eisenstein series

Crossrefs

Cf. A037164.

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (E_12), A058550 (E_14), A029829 (E_16), A029830 (E_20), A029831 (E_24).

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(12);

Mathematica

Table[If[n == 0, 691, 65520 DivisorSigma[11, n]], {n, 0, 16}] (* Jean-François Alcover, Feb 26 2018 *)

PARI

a(n)=if(n<1,691*(n==0),65520*sigma(n,11))