A279893 Eisenstein series E_22(q) (alternate convention E_11(q)), multiplied by 77683.

77683, -552, -1157628456, -5774114968608, -2427722831757864, -263214111328125552, -12109202528761173024, -308317316973972772416, -5091303792066668003880, -60399282006368937251976, -552000263214112485753456, -4084937969230504375869024, -25394838301602325644596256, -136379620048544616772836528, -646588586243917921590531648

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), A279892 (43867*E_18), A029830 (174611*E_20), this sequence (77683*E_22), A029831 (236364091*E_24).

Cf. A282047 (E_4^4*E_6), A282328 (E_4*E_6^3).

Programs

Mathematica

terms = 15;
E22[x_] = 77683 - 552*Sum[k^21*x^k/(1 - x^k), {k, 1, terms}];
E22[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

G.f.: 77683 - 552 * Sum_{i>=1} sigma_21(i)q^i where sigma_21(n) is A013969.

a(n) = 57183*A282047(n) + 20500*A282328(n). - Seiichi Manyama, Feb 12 2017