A029830 - OEIS

%I #23 Feb 27 2018 07:51:46

%S 174611,13200,6920614800,15341851377600,3628395292275600,

%T 251770019531263200,8043563916910526400,150465416446925500800,

%U 1902324110996589786000,17831242688625346952400,132000251770026451864800,807299993919072011054400,4217144038884527916580800,19297347832955888660949600

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

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

%H Seiichi Manyama, <a href="/A029830/b029830.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Ed#Eisen">Index entries for sequences related to Eisenstein series</a>

%F a(n) = 53361*A282015(n) + 121250*A282292(n). - _Seiichi Manyama_, Feb 11 2017

%t terms = 14;

%t E20[x_] = 174611 + 13200*Sum[k^19*x^k/(1 - x^k), {k, 1, terms}];

%t E20[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)

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

%Y 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).

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

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_