A008699 Theta series of Niemeier lattice of type A_6^4.

1, 168, 192528, 16815456, 397786704, 4630192560, 34416639936, 187487122368, 814893967440, 2975532395976, 9486531825120, 27053035734816, 70486174680768, 169930998266736, 384163653863808

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 - A008698, A008700 - 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 = 49/72 E4[q]^3 + 23/72 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 (49*E_4(z)^3 + 23*E_6(z)^2)/72. - Daniel D. Briggs, Nov 25 2011