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.

A008696 Theta series of Niemeier lattice of type D_6^4.

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%I A008696 #30 Sep 14 2022 08:25:53
%S A008696 1,240,190800,16833600,397680720,4630540320,34416204480,187485916800,
%T A008696 814900050000,2975524213680,9486523478880,27053074226880,
%U A008696 70486147972800,169930956669600,384163682797440,820166912933760
%N A008696 Theta series of Niemeier lattice of type D_6^4.
%C A008696 Also the theta series for the Niemeier lattice of type A_9^2 D_6. - clarified by _Ben Mares_, Sep 13 2022
%D A008696 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H A008696 G. C. Greubel, <a href="/A008696/b008696.txt">Table of n, a(n) for n = 0..1000</a>
%F A008696 This series is the q-expansion of (13*E_4(z)^3 + 5*E_6(z)^2)/18. - _Daniel D. Briggs_, Nov 25 2011
%t A008696 terms = 15; th = EllipticTheta; E4 = 1 + 240*Sum[k^3*(q^k/(1 - q^k)), {k, 1, terms}] + O[q]^terms; E6 = th[2, 0, q]^12 + th[3, 0, q]^12 - 33*th[2, 0, q]^4*th[3, 0, q]^4*(th[2, 0, q]^4 + th[3, 0, q]^4); CoefficientList[ (13/18)*E4^3 + (5/18)*E6^2 + O[q]^terms, q] (* _Jean-François Alcover_, Jul 05 2017 *)
%Y A008696 Cf. A004009, A013973.
%Y A008696 Cf. A008688 - A008695, A008697 - A008704.
%K A008696 nonn
%O A008696 0,2
%A A008696 _N. J. A. Sloane_