A008704 Theta series of Niemeier lattice of type A_1^24.

1, 48, 195408, 16785216, 397963344, 4629612960, 34417365696, 187489131648, 814883829840, 2975546033136, 9486545735520, 27052971581376, 70486219194048, 169931067595296, 384163605641088

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 - A008703.

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 = 11/18 E4[q]^3 + 7/18 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 (11*E_4(z)^3 + 7*E_6(z)^2)/18. - Daniel D. Briggs, Nov 26 2011