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%I #25 Oct 26 2023 08:31:29
%S 1,0,252,3136,17388,64512,194656,501120,1101996,2193408,4195800,
%T 7551936,12508384,19934208,31616064,48487040,70404012,99735552,
%U 142513308,200515392,268608312,353783808,475911072
%N Theta series of 14-dimensional unimodular lattice (E7+E7)+.
%H J. H. Conway, A. M. Odlyzko, and N. J. A. Sloane, <a href="http://dx.doi.org/10.1112/S0025579300009244">Extremal Self-Dual Lattices Exist Only in Dimensions 1-8, 12, 14, 15, 23 and 24</a>, Mathematika, 25 (1978), 36-43.
%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; 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/U14.html">Home page for this lattice</a>.
%F G.f.: (theta3^7 + 7*theta3^3*theta2^4)^2 + (theta2^7 + 7*theta2^3*theta3^4)^2.
%e 1 + 252*q^2 + 3136*q^3 + ...
%t terms = 23; s = (EllipticTheta[3, 0, q]^7 + 7*EllipticTheta[3, 0, q]^3 * EllipticTheta[2, 0, q]^4)^2 + (EllipticTheta[2, 0, q]^7 + 7*EllipticTheta[2, 0, q]^3 * EllipticTheta[3, 0, q]^4)^2 + O[q]^terms // Normal; Join[{1, 0}, Rest[(List @@ s) /. q -> 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 07 2017 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_
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