A008703 Theta series of Niemeier lattice of type A_2^12.

1, 72, 194832, 16791264, 397928016, 4629728880, 34417220544, 187488729792, 814885857360, 2975543305704, 9486542953440, 27052984412064, 70486210291392, 169931053729584, 384163615285632

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 - A008702, 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 = 5/8 E4[q]^3 + 3/8 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 (5*E_4(z)^3 + 3*E_6(z)^2)/8. - Daniel D. Briggs, Nov 25 2011