A008694 Theta series of Niemeier lattice of type A_12^2.

1, 312, 189072, 16851744, 397574736, 4630888080, 34415769024, 187484711232, 814906132560, 2975516031384, 9486515132640, 27053112718944, 70486121264832, 169930915072464, 384163711731072

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 - A008693, A008695 - 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 = 55/72 E4[q]^3 + 17/72 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 (55*E_4(z)^3 + 17*E_6(z)^2)/72. - Daniel D. Briggs, Nov 25 2011