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A029828 Eisenstein series E_12(q) (alternate convention E_6(q)), multiplied by 691. 27


%S 691,65520,134250480,11606736960,274945048560,3199218815520,

%T 23782204031040,129554448266880,563087459516400,2056098632318640,

%U 6555199353000480,18693620658498240,48705965462306880,117422349017369760,265457064498837120,566735214731736960,1153203117089652720

%N Eisenstein series E_12(q) (alternate convention E_6(q)), multiplied by 691.

%D R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 53.

%D N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 1984, see p. 111.

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

%H Seiichi Manyama, <a href="/A029828/b029828.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>

%p E := proc(k) local n,t1; t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n,n=1..60); series(t1,q,60); end; E(12);

%t Table[If[n == 0, 691, 65520 DivisorSigma[11, n]], {n, 0, 16}] (* _Jean-Fran├žois Alcover_, Feb 26 2018 *)

%o (PARI) a(n)=if(n<1,691*(n==0),65520*sigma(n,11))

%Y Cf. A037164.

%Y Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (E_12), A058550 (E_14), A029829 (E_16), A029830 (E_20), A029831 (E_24).

%K nonn

%O 0,1

%A _N. J. A. Sloane_

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Last modified September 18 22:25 EDT 2020. Contains 337174 sequences. (Running on oeis4.)