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%I #13 Feb 26 2018 09:14:05
%S 1,-24,-196632,-38263776,-1610809368,-29296875024,-313495116768,
%T -2325336249792,-13195750342680,-61004818143672,-240029297071632,
%U -828545091454368,-2568152034827232,-7269002558214096,-19051479894545856,-46708710975763776
%N Eisenstein series E_14(q) (alternate convention E_7(q)).
%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 Seiichi Manyama, <a href="/A058550/b058550.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(14);
%t terms = 16;
%t E14[x_] = 1 - 24*Sum[k^13*x^k/(1 - x^k), {k, 1, terms}];
%t E14[x] + O[x]^terms // CoefficientList[#, x]&
%t (* or: *)
%t Table[If[n == 0, 1, -24*DivisorSigma[13, n]], {n, 0, terms-1}] (* _Jean-François Alcover_, Feb 26 2018 *)
%o (PARI) a(n)=if(n<1,n==0,-24*sigma(n,13))
%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 sign
%O 0,2
%A _N. J. A. Sloane_, Dec 25 2000