A008690 Theta series of Niemeier lattice of type D_12^2.

1, 528, 183888, 16906176, 397256784, 4631931360, 34414462656, 187481094528, 814924380240, 2975491484496, 9486490093920, 27053228195136, 70486041140928, 169930790281056, 384163798531968

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, A008691 - 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 = 8/9 E4[q]^3 + 1/9 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 8/9 E_4(z)^3 + 1/9 E_6(z)^2. See A004009 and A013973. - Daniel D. Briggs, Nov 25 2011