A008692 Theta series of Niemeier lattice of type A_15 D_9.

1, 384, 187344, 16869888, 397468752, 4631235840, 34415333568, 187483505664, 814912215120, 2975507849088, 9486506786400, 27053151211008, 70486094556864, 169930873475328, 384163740664704

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. A008688, A008689, A008690, A008691, A008693 - 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 = 29/36 E4[q]^3 + 7/36 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 (29*E_4(z)^3 + 7*E_6(z)^2)/36. See A004009 and A013973. - Daniel D. Briggs, Nov 25 2011