A008701 Theta series of Niemeier lattice of type A_4^6.

1, 120, 193680, 16803360, 397857360, 4629960720, 34416930240, 187487926080, 814889912400, 2975537850840, 9486537389280, 27053010073440, 70486192486080, 169931025998160, 384163634574720

Offset

0,2

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

Formula

This series is the q-expansion of (47*E_4(z)^3 + 25*E_6(z)^2)/72. - Daniel D. Briggs, Nov 25 2011

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 = 47/72 E4[q]^3 + 25/72 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)

Crossrefs

Cf. A004009, A013973.

Cf. A008688 - A008700, A008702, A008703, A008704.

Sequence in context: A068296 A123380 A172805 * A158043 A009767 A181750

Adjacent sequences: A008698 A008699 A008700 * A008702 A008703 A008704

Keyword

nonn

Author

N. J. A. Sloane

Status

approved