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%I #15 Feb 27 2018 10:53:09
%S 1,16320,534790080,234174178560,17524001357760,498046875016320,
%T 7673653657232640,77480203842286080,574226476491096000,
%U 3360143509958850240,16320498047409790080,68172690124863440640,251450283274373326080
%N Numerators of q-expansion of Eisenstein series E_16(q).
%C Denominators are 3617 except for leading term for which denominator is 1.
%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.
%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(16);
%t terms = 13; E16[x_] = 1 - (32/BernoulliB[16])*Sum[k^15*(x^k/(1 - x^k)), {k, 1, terms}]; E16[x] + O[x]^terms // CoefficientList[#, x]& // Numerator (* _Jean-François Alcover_, Feb 27 2018 *)
%Y Cf. A029829.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Dec 25 2000