A029829 Eisenstein series E_16(q) (alternate convention E_8(q)), multiplied by 3617.

3617, 16320, 534790080, 234174178560, 17524001357760, 498046875016320, 7673653657232640, 77480203842286080, 574226476491096000, 3360143509958850240, 16320498047409790080, 68172690124863440640

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• 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. A058552.

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(16);

Mathematica

terms = 12;
E16[x_] = 3617 + 16320*Sum[k^15*x^k/(1 - x^k), {k, 1, terms}];
E16[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)

PARI

a(n)=if(n<1,3617*(n==0),16320*sigma(n,15))

Formula

a(n) = 1617*A282012(n) + 2000*A282287(n). - Seiichi Manyama, Feb 11 2017