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%I #20 Dec 13 2017 02:47:32
%S 1,16,368,448,3184,2016,10304,5504,25712,12112,46368,21312,89152,
%T 35168,126592,56448,205936,78624,278576,109760,401184,154112,490176,
%U 194688,719936,252016,808864,327040
%N Theta series of {D_8}* lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.
%H G. C. Greubel, <a href="/A008427/b008427.txt">Table of n, a(n) for n = 0..10000</a>
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0509316">On the Integrality of n-th Roots of Generating Functions</a>, arXiv:math/0509316 [math.NT], 2005-2006.
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://doi.org/10.1016/j.jcta.2006.03.018">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Ds8.html">Home page for this lattice</a>
%F G.f.: (theta_3(q))^8 + (theta_2(q))^8.
%t terms = 28; s = EllipticTheta[3, 0, q]^8 + EllipticTheta[2, 0, q]^8 + O[q]^terms; CoefficientList[s, q] (* _Jean-François Alcover_, Jul 04 2017 *)
%Y Cf. A008430, A109772.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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