A008702 Theta series of Niemeier lattice of type A_3^8.

1, 96, 194256, 16797312, 397892688, 4629844800, 34417075392, 187488327936, 814887884880, 2975540578272, 9486540171360, 27052997242752, 70486201388736, 169931039863872, 384163624930176

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. A004009, A013973.

Cf. A008688 - A008701, A008703, A008704.

Programs

Mathematica

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 = 23/36 E4[q]^3 + 13/36 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)

Formula

This series is the q-expansion of (23*E_4(z)^3 + 13*E_6(z)^2)/36. - Daniel D. Briggs, Nov 26 2011