A014747 Theta series of lattice D20+.

1, 0, 760, 0, 77560, 524288, 2508000, 10485760, 34729720, 99614720, 259114704, 608174080, 1327461600, 2739404800, 5341699520, 9921626112, 17701924600, 30592204800, 51294999960, 83277905920, 131880275664

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..2500 from G. C. Greubel)

Crossrefs

Cf. A022051.

Programs

Mathematica

terms = 21; s = 1/2 (EllipticTheta[2, 0, q]^20 + EllipticTheta[3, 0, q]^20 + EllipticTheta[4, 0, q]^20) + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 07 2017 *)

Formula

G.f.: (theta2(q)^20 + theta3(q)^20 + theta4(q)^20)/2.