cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A029829 Eisenstein series E_16(q) (alternate convention E_8(q)), multiplied by 3617.

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%I A029829 #20 Feb 27 2018 07:09:07
%S A029829 3617,16320,534790080,234174178560,17524001357760,498046875016320,
%T A029829 7673653657232640,77480203842286080,574226476491096000,
%U A029829 3360143509958850240,16320498047409790080,68172690124863440640
%N A029829 Eisenstein series E_16(q) (alternate convention E_8(q)), multiplied by 3617.
%D A029829 N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 1984, see p. 111.
%D A029829 J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.
%H A029829 Seiichi Manyama, <a href="/A029829/b029829.txt">Table of n, a(n) for n = 0..10000</a>
%H A029829 <a href="/index/Ed#Eisen">Index entries for sequences related to Eisenstein series</a>
%F A029829 a(n) = 1617*A282012(n) + 2000*A282287(n). - _Seiichi Manyama_, Feb 11 2017
%p A029829 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 A029829 terms = 12;
%t A029829 E16[x_] = 3617 + 16320*Sum[k^15*x^k/(1 - x^k), {k, 1, terms}];
%t A029829 E16[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)
%o A029829 (PARI) a(n)=if(n<1,3617*(n==0),16320*sigma(n,15))
%Y A029829 Cf. A058552.
%Y A029829 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 A029829 nonn
%O A029829 0,1
%A A029829 _N. J. A. Sloane_