A002434 Theta series of Borcherds' 27-dimensional unimodular lattice T_27.

1, 0, 0, 1640, 119574, 1497600, 16733184, 108081792, 588805308, 2544826368, 9516533760, 31328289720, 92876121704, 252846217728, 638250227712, 1511780699520, 3387237774102, 7228330481664

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• 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.
• J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, Preface to 3rd ed.

Programs

Maple

th3^27-54*th3^19*delta8+216*th3^11*delta8^2-1024*th3^3*delta8^3 # (th3= A000122, delta8= A002408).

Mathematica

terms = 18; QP = QPochhammer; th3 = EllipticTheta[3, 0, q]; delta8 = q*(QP[q]*(QP[q^4]/QP[q^2]))^8; s = th3^27 - 54*th3^19*delta8 + 216*th3^11*delta8^2 - 1024*th3^3*delta8^3 + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 06 2017 *)