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A037164 Numerators of coefficients of Eisenstein series E_12(q) (or E_6(q) or E_24(q)).

%I A037164 #28 Jul 08 2025 22:03:31
%S A037164 1,65520,134250480,11606736960,274945048560,3199218815520,
%T A037164 23782204031040,129554448266880,563087459516400,2056098632318640,
%U A037164 6555199353000480,18693620658498240,48705965462306880,117422349017369760,265457064498837120,566735214731736960,1153203117089652720
%N A037164 Numerators of coefficients of Eisenstein series E_12(q) (or E_6(q) or E_24(q)).
%C A037164 First denominator is 1, rest are 691.
%D A037164 R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 53.
%D A037164 N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 1984, see p. 111.
%D A037164 J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.
%H A037164 Andy Huchala, <a href="/A037164/b037164.txt">Table of n, a(n) for n = 0..20000</a>
%H A037164 H. D. Nguyen, D. Taggart, <a href="https://citeseerx.ist.psu.edu/pdf/8f2f36f22878c984775ed04368b8893879b99458">Mining the OEIS: Ten Experimental Conjectures</a>, 2013; Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
%H A037164 <a href="/index/Ed#Eisen">Index entries for sequences related to Eisenstein series</a>
%p A037164 with(numtheory):
%p A037164 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);
%p A037164 seq(numer(coeff(%,q,n)), n=0..24);
%t A037164 terms = 13; E12[x_] = 1 - (24/BernoulliB[12])*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}]; E12[x] + O[x]^terms // CoefficientList[#, x]& // Numerator (* _Jean-François Alcover_, Feb 27 2018 *)
%o A037164 (Sage)
%o A037164 l = list(eisenstein_series_qexp(12,20, normalization='integral'))
%o A037164 l[0] = 1; l # _Andy Huchala_, Jul 01 2021
%Y A037164 Cf. A029828.
%K A037164 nonn,frac,easy
%O A037164 0,2
%A A037164 _N. J. A. Sloane_