A008427 Theta series of {D_8}* lattice.

1, 16, 368, 448, 3184, 2016, 10304, 5504, 25712, 12112, 46368, 21312, 89152, 35168, 126592, 56448, 205936, 78624, 278576, 109760, 401184, 154112, 490176, 194688, 719936, 252016, 808864, 327040

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.
• N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
• G. Nebe and N. J. A. Sloane, Home page for this lattice

Crossrefs

Cf. A008430, A109772.

Programs

Mathematica

terms = 28; s = EllipticTheta[3, 0, q]^8 + EllipticTheta[2, 0, q]^8 + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 04 2017 *)

Formula

G.f.: (theta_3(q))^8 + (theta_2(q))^8.