OFFSET
0,4
REFERENCES
R. E. Borcherds, The Leech Lattice and Other Lattices, Ph. D. Dissertation, Cambridge Univ., 1984.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Third Ed., pp. xli-xlii.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
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.
FORMULA
Let f = theta_3, g = 8-dimensional cusp form [Conway-Sloane, p. 187, Eqs. (32)-(34)]. The theta-series is f^26 - 52*f^18*g + 156*f^10*g^2.
EXAMPLE
1 + 3120*q^3 + 102180*q^4 + 1482624*q^5 + 13191360*q^6 + 83859360*q^7 + 416587860*q^8 + ...
MATHEMATICA
terms = 22; QP = QPochhammer; f = EllipticTheta[3, 0, q]; g = q*(QP[q]*(QP[q^4]/QP[q^2]))^8; s = f^26 - 52*f^18*g + 156*f^10*g^2 + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 06 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar
STATUS
approved