A002519 Theta series of 28-dimensional unimodular lattice with no roots and a parity vector of norm 4.

1, 0, 0, 1728, 106472, 1734912, 19335168, 141575552, 805208040, 3725209088, 14647517184, 50579062848, 156715230240, 443680116992, 1162915024896, 2851005884544, 6596700471272, 14509559545344, 30507866603520

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

R. Bacher and B. B. Venkov, Réseaux entiers unimodulaires sans racine en dimension 27 et 28, in Réseaux euclidiens, designs sphériques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.

Formula

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.

Mathematica

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 *)

Crossrefs

Cf. A002520.

Sequence in context: A017523 A237490 A223324 * A052068 A289210 A289209

Adjacent sequences: A002516 A002517 A002518 * A002520 A002521 A002522

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 04 2000

Status

approved