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%I #20 Feb 27 2018 07:09:07
%S 3617,16320,534790080,234174178560,17524001357760,498046875016320,
%T 7673653657232640,77480203842286080,574226476491096000,
%U 3360143509958850240,16320498047409790080,68172690124863440640
%N Eisenstein series E_16(q) (alternate convention E_8(q)), multiplied by 3617.
%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="/A029829/b029829.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) = 1617*A282012(n) + 2000*A282287(n). - _Seiichi Manyama_, Feb 11 2017
%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 = 12;
%t E16[x_] = 3617 + 16320*Sum[k^15*x^k/(1 - x^k), {k, 1, terms}];
%t E16[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)
%o (PARI) a(n)=if(n<1,3617*(n==0),16320*sigma(n,15))
%Y Cf. A058552.
%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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