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.

A008694 Theta series of Niemeier lattice of type A_12^2.

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%I A008694 #17 Mar 04 2020 13:48:00
%S A008694 1,312,189072,16851744,397574736,4630888080,34415769024,187484711232,
%T A008694 814906132560,2975516031384,9486515132640,27053112718944,
%U A008694 70486121264832,169930915072464,384163711731072
%N A008694 Theta series of Niemeier lattice of type A_12^2.
%D A008694 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H A008694 G. C. Greubel, <a href="/A008694/b008694.txt">Table of n, a(n) for n = 0..1000</a>
%F A008694 This series is the q-expansion of (55*E_4(z)^3 + 17*E_6(z)^2)/72. - _Daniel D. Briggs_, Nov 25 2011
%t A008694 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 = 55/72 E4[q]^3 + 17/72 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 06 2017 *)
%Y A008694 Cf. A004009, A013973.
%Y A008694 Cf. A008688 - A008693, A008695 - A008704.
%K A008694 nonn
%O A008694 0,2
%A A008694 _N. J. A. Sloane_