A008688 Theta series of Niemeier lattice of type D_24.

1, 1104, 170064, 17051328, 396408912, 4634713440, 34410979008, 187471449984, 814973040720, 2975426026128, 9486423324000, 27053536131648, 70485827477184, 169930457503968, 384164030001024

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. 407.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A008689 - A008704.

Programs

Mathematica

(* Coefficients 11/9 and -2/9 were computed from the data. *)
terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 11/9 E4[q]^3 - 2/9 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)