A058550 Eisenstein series E_14(q) (alternate convention E_7(q)).

1, -24, -196632, -38263776, -1610809368, -29296875024, -313495116768, -2325336249792, -13195750342680, -61004818143672, -240029297071632, -828545091454368, -2568152034827232, -7269002558214096, -19051479894545856, -46708710975763776

Offset: 0

Author

N. J. A. Sloane, Dec 25 2000

Keywords

• sign

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

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

Crossrefs

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(14);

Mathematica

terms = 16;
E14[x_] = 1 - 24*Sum[k^13*x^k/(1 - x^k), {k, 1, terms}];
E14[x] + O[x]^terms // CoefficientList[#, x]&
(* or: *)
Table[If[n == 0, 1, -24*DivisorSigma[13, n]], {n, 0, terms-1}] (* Jean-François Alcover, Feb 26 2018 *)
(* or *)
terms = 15; E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}]; E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}]; CoefficientList[Series[E4[x]^2*E6[x], {x, 0, terms}], x] (* Vaclav Kotesovec, Aug 03 2025 *)

PARI

a(n)=if(n<1,n==0,-24*sigma(n,13))