%I #33 Feb 26 2018 10:19:06
%S 43867,-28728,-3765465144,-3709938631392,-493547047383096,
%T -21917724609403728,-486272786232443616,-6683009405824511424,
%U -64690198594597187640,-479102079577959825624,-2872821917728374840144,-14520482234727711482016,-63736746640768788267744
%N Eisenstein series E_18(q) (alternate convention E_9(q)), multiplied by 43867.
%D J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.
%H Seiichi Manyama, <a href="/A279892/b279892.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: 43867 - 28728 * Sum_{i>=1} sigma_17(i)q^i where sigma_17(n) is A013965.
%F a(n) = 38367*A282000(n) + 5500*A282253(n). - _Seiichi Manyama_, Feb 11 2017
%t terms = 13;
%t E18[x_] = 43867 - 28728*Sum[k^17*x^k/(1 - x^k), {k, 1, terms}];
%t E18[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), this sequence (43867*E_18), A029830 (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24).
%Y Cf. A282000 (E_4^3*E_6), A282253 (E_6^3).
%K sign
%O 0,1
%A _Seiichi Manyama_, Dec 22 2016