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A022065
Theta series of D*_12 lattice.
2
1, 24, 264, 5856, 7944, 75024, 64416, 403392, 253704, 1423032, 825264, 3865248, 1938336, 8911056, 4437312, 18305856, 8118024, 34076592, 15653352, 59426400, 24832944, 98427648, 42517728, 154472256, 61903776, 234450024, 98021616, 345796800, 133522752, 492267600
OFFSET
0,2
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.
LINKS
G. Nebe and N. J. A. Sloane, Home page for this lattice
FORMULA
Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (9/8) * Pi^3 / Gamma(3/4)^12 = A388243. - Simon Plouffe, Sep 15 2025
EXAMPLE
G.f. = 1 + 24*q^2 + 264*q^4 + ...
PROG
(SageMath)
L = [1, 24]
M = ModularForms(Gamma0(2), 6)
bases = [_.q_expansion(20) for _ in M.integral_basis()]
f = sum(x*y for (x, y) in zip(bases, L)); list(f) # Andy Huchala, Jul 13 2021
CROSSREFS
Sequence in context: A000145 A126904 A001413 * A125412 A270846 A187048
KEYWORD
nonn
STATUS
approved