%I #24 Oct 17 2023 05:44:05
%S 1,0,0,1728,106472,1734912,19335168,141575552,805208040,3725209088,
%T 14647517184,50579062848,156715230240,443680116992,1162915024896,
%U 2851005884544,6596700471272,14509559545344,30507866603520
%N Theta series of 28-dimensional unimodular lattice with no roots and a parity vector of norm 4.
%H Vaclav Kotesovec, <a href="/A002519/b002519.txt">Table of n, a(n) for n = 0..2000</a>
%H R. Bacher and B. B. Venkov, <a href="https://www-fourier.univ-grenoble-alpes.fr/?q=fr/content/reseaux-entiers-unimodulaires-sans-racine-en-dimension-27-et-28">Réseaux entiers unimodulaires sans racine en dimension 27 et 28</a>, in Réseaux euclidiens, designs sphériques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.
%F G.f.: t3^28 - 56*t3^20*D8 + 280*t3^12*D8^2 - 512*t3^4*D8^3 where t3 = theta3(z) and D8 = (theta2(z)*theta4(z))^4/16.
%t terms = 19; t2 = EllipticTheta[2, 0, z]; t3 = EllipticTheta[3, 0, z]; t4 = EllipticTheta[4, 0, z]; D8 = (t2*t4)^4/16; s = t3^28 - 56*t3^20*D8 + 280*t3^12*D8^2 - 512*t3^4*D8^3 + O[z]^terms; CoefficientList[s, z] (* _Jean-François Alcover_, Jul 06 2017 *)
%Y Cf. A002520.
%K nonn
%O 0,4
%A _N. J. A. Sloane_
%E More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 04 2000