%I #32 Feb 26 2018 10:49:29
%S 77683,-552,-1157628456,-5774114968608,-2427722831757864,
%T -263214111328125552,-12109202528761173024,-308317316973972772416,
%U -5091303792066668003880,-60399282006368937251976,-552000263214112485753456,-4084937969230504375869024,-25394838301602325644596256,-136379620048544616772836528,-646588586243917921590531648
%N Eisenstein series E_22(q) (alternate convention E_11(q)), multiplied by 77683.
%D J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.
%H Seiichi Manyama, <a href="/A279893/b279893.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: 77683 - 552 * Sum_{i>=1} sigma_21(i)q^i where sigma_21(n) is A013969.
%F a(n) = 57183*A282047(n) + 20500*A282328(n). - _Seiichi Manyama_, Feb 12 2017
%t terms = 15;
%t E22[x_] = 77683 - 552*Sum[k^21*x^k/(1 - x^k), {k, 1, terms}];
%t E22[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%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), A029830 (174611*E_20), this sequence (77683*E_22), A029831 (236364091*E_24).
%Y Cf. A282047 (E_4^4*E_6), A282328 (E_4*E_6^3).
%K sign
%O 0,1
%A _Seiichi Manyama_, Dec 22 2016