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.

A008702 Theta series of Niemeier lattice of type A_3^8.

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%I A008702 #17 Mar 04 2020 14:55:13
%S A008702 1,96,194256,16797312,397892688,4629844800,34417075392,187488327936,
%T A008702 814887884880,2975540578272,9486540171360,27052997242752,
%U A008702 70486201388736,169931039863872,384163624930176
%N A008702 Theta series of Niemeier lattice of type A_3^8.
%D A008702 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H A008702 G. C. Greubel, <a href="/A008702/b008702.txt">Table of n, a(n) for n = 0..1000</a>
%F A008702 This series is the q-expansion of (23*E_4(z)^3 + 13*E_6(z)^2)/36. - _Daniel D. Briggs_, Nov 26 2011
%t A008702 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 = 23/36 E4[q]^3 + 13/36 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 06 2017 *)
%Y A008702 Cf. A004009, A013973.
%Y A008702 Cf. A008688 - A008701, A008703, A008704.
%K A008702 nonn
%O A008702 0,2
%A A008702 _N. J. A. Sloane_