A029831 - OEIS

%I #18 Feb 27 2018 07:09:04

%S 236364091,131040,1099243323360,12336522153621120,9221121336284413920,

%T 1562118530273437631040,103486260766565509822080,

%U 3586400651444203277717760,77352372210526124884754400,1161399411211600265764157280

%N Eisenstein series E_24(q) (alternate convention E_12(q)), multiplied by 236364091.

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

%H Seiichi Manyama, <a href="/A029831/b029831.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) = 49679091*A282330(n) + 176400000*A282332(n) + 10285000*A282331(n). - _Seiichi Manyama_, Feb 12 2017

%t terms = 10;

%t E24[x_] = 236364091 + 131040*Sum[k^23*x^k/(1 - x^k), {k, 1, terms}];

%t E24[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)

%o (PARI) a(n)=if(n<1,236364091*(n==0),131040*sigma(n,23))

%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), A279893 (77683*E_22), this sequence (236364091*E_24).

%Y Cf. A282330 (E_4^6), A282332 (E_4^3*E_6^2), A282331 (E_6^4).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_