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.

A008695 Theta series of Niemeier lattice of type A_11 D_7 E_6.

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%I A008695 #28 Sep 14 2022 08:25:59
%S A008695 1,288,189648,16845696,397610064,4630772160,34415914176,187485113088,
%T A008695 814904105040,2975518758816,9486517914720,27053099888256,
%U A008695 70486130167488,169930928938176,384163702086528
%N A008695 Theta series of Niemeier lattice of type A_11 D_7 E_6.
%C A008695 Also the theta series of the Niemeier lattice of type E_6^4. - clarified by _Ben Mares_, Sep 13 2022
%D A008695 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H A008695 G. C. Greubel, <a href="/A008695/b008695.txt">Table of n, a(n) for n = 0..1000</a>
%F A008695 This series is the q-expansion of (3*E_4(z)^3 + E_6(z)^2)/4. - _Daniel D. Briggs_, Nov 25 2011
%t A008695 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[ (3/4)*E4^3 + (1/4)*E6^2 + O[q]^terms, q] (* _Jean-François Alcover_, Jul 05 2017 *)
%Y A008695 Cf. A004009, A013973.
%Y A008695 Cf. A008688 - A008694, A008696 - A008704.
%K A008695 nonn
%O A008695 0,2
%A A008695 _N. J. A. Sloane_