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.

A008697 Theta series of Niemeier lattice of type A_8^3.

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%I A008697 #17 Mar 04 2020 18:10:55
%S A008697 1,216,191376,16827552,397716048,4630424400,34416349632,187486318656,
%T A008697 814898022480,2975526941112,9486526260960,27053061396192,
%U A008697 70486156875456,169930970535312,384163673152896
%N A008697 Theta series of Niemeier lattice of type A_8^3.
%D A008697 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H A008697 G. C. Greubel, <a href="/A008697/b008697.txt">Table of n, a(n) for n = 0..1000</a>
%F A008697 This series is the q-expansion of (17*E_4(z)^3 + 7*E_6(z)^2)/24. - _Daniel D. Briggs_, Nov 25 2011
%t A008697 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 = 17/24 E4[q]^3 + 7/24 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 06 2017 *)
%Y A008697 Cf. A004009, A013973.
%Y A008697 Cf. A008688 - A008696, A008698 - A008704.
%K A008697 nonn
%O A008697 0,2
%A A008697 _N. J. A. Sloane_