A279892 Eisenstein series E_18(q) (alternate convention E_9(q)), multiplied by 43867.

43867, -28728, -3765465144, -3709938631392, -493547047383096, -21917724609403728, -486272786232443616, -6683009405824511424, -64690198594597187640, -479102079577959825624, -2872821917728374840144, -14520482234727711482016, -63736746640768788267744

Offset: 0

Author

Seiichi Manyama, Dec 22 2016

Keywords

• sign

References

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (691*E_12), A058550 (E_14), A029829 (3617*E_16), this sequence (43867*E_18), A029830 (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24).

Cf. A282000 (E_4^3*E_6), A282253 (E_6^3).

Programs

Mathematica

terms = 13;
E18[x_] = 43867 - 28728*Sum[k^17*x^k/(1 - x^k), {k, 1, terms}];
E18[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

G.f.: 43867 - 28728 * Sum_{i>=1} sigma_17(i)q^i where sigma_17(n) is A013965.

a(n) = 38367*A282000(n) + 5500*A282253(n). - Seiichi Manyama, Feb 11 2017