A008698 Theta series of Niemeier lattice of type A_7^2 D_5^2.

1, 192, 191952, 16821504, 397751376, 4630308480, 34416494784, 187486720512, 814895994960, 2975529668544, 9486529043040, 27053048565504, 70486165778112, 169930984401024, 384163663508352

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 - A008697, A008699 - 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 = 25/36 E4[q]^3 + 11/36 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 (25*E_4(z)^3 + 11*E_6(z)^2)/36. - Daniel D. Briggs, Nov 25 2011