%I #23 Oct 14 2023 23:48:41
%S 1,0,0,261120,18947520,535818240,8320327680,83347937280,622558664640,
%T 3614759362560,17694184734720,73337844372480,272615629589760,
%U 898646461378560,2752654757806080,7687895624386560
%N Theta series of 32-dimensional Quebbemann lattice Q_32.
%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="http://dx.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/Q32.html">Home page for this lattice</a>.
%H H.-G. Quebbemann, <a href="http://dx.doi.org/10.1016/0021-8693(87)90208-0">Lattices with theta-functions for G(sqrt(2)) and linear codes</a>, J. Algebra, 105 (1987), 443-450.
%H H.-G. Quebbemann, <a href="http://dx.doi.org/10.1006/jnth.1995.1111">Modular lattices in Euclidean spaces</a>, J. Number Theory, 54 (1995), 190-202.
%F G.f.: b(x)^8 - 192*b(x)^4*d(x) + 576*d(x)^2 where b(x) is the g.f. of A004011 and d(x) is the g.f. of A002288. - _Sean A. Irvine_, Jul 26 2020
%K nonn
%O 0,4
%A _N. J. A. Sloane_