A029830 Eisenstein series E_20(q) (alternate convention E_10(q)), multiplied by 174611.

174611, 13200, 6920614800, 15341851377600, 3628395292275600, 251770019531263200, 8043563916910526400, 150465416446925500800, 1902324110996589786000, 17831242688625346952400, 132000251770026451864800, 807299993919072011054400, 4217144038884527916580800, 19297347832955888660949600

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• 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. 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), this sequence (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24).

Cf. A282015 (E_4^5), A282292 (E_4^2*E_6^2 = E_10^2).

Programs

Mathematica

terms = 14;
E20[x_] = 174611 + 13200*Sum[k^19*x^k/(1 - x^k), {k, 1, terms}];
E20[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)

PARI

a(n)=if(n<1,174611*(n==0),13200*sigma(n,19))

Formula

a(n) = 53361*A282015(n) + 121250*A282292(n). - Seiichi Manyama, Feb 11 2017