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.

A008689 Theta series of Niemeier lattice of type A_24.

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%I A008689 #20 Mar 04 2020 07:39:20
%S A008689 1,600,182160,16924320,397150800,4632279120,34414027200,187479888960,
%T A008689 814930462800,2975483302200,9486481747680,27053266687200,
%U A008689 70486014432960,169930748683920,384163827465600
%N A008689 Theta series of Niemeier lattice of type A_24.
%D A008689 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H A008689 G. C. Greubel, <a href="/A008689/b008689.txt">Table of n, a(n) for n = 0..1000</a>
%F A008689 a(n) = A023936(25n). - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Aug 02 2001
%F A008689 This series is the q-expansion of 67/72 E_4(z)^3 + 5/72 E_6(z)^2. - _Daniel D. Briggs_, Nov 25 2011
%t A008689 terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 67/72 E4[q]^3 + 5/72 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 06 2017 *)
%Y A008689 Cf. A004009, A013973, A023936.
%K A008689 nonn
%O A008689 0,2
%A A008689 _N. J. A. Sloane_