A008696 Theta series of Niemeier lattice of type D_6^4.

1, 240, 190800, 16833600, 397680720, 4630540320, 34416204480, 187485916800, 814900050000, 2975524213680, 9486523478880, 27053074226880, 70486147972800, 169930956669600, 384163682797440, 820166912933760

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Also the theta series for the Niemeier lattice of type A_9^2 D_6. - clarified by Ben Mares, Sep 13 2022

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 - A008695, A008697 - A008704.

Programs

Mathematica

terms = 15; th = EllipticTheta; E4 = 1 + 240*Sum[k^3*(q^k/(1 - q^k)), {k, 1, terms}] + O[q]^terms; E6 = th[2, 0, q]^12 + th[3, 0, q]^12 - 33*th[2, 0, q]^4*th[3, 0, q]^4*(th[2, 0, q]^4 + th[3, 0, q]^4); CoefficientList[ (13/18)*E4^3 + (5/18)*E6^2 + O[q]^terms, q] (* Jean-François Alcover, Jul 05 2017 *)

Formula

This series is the q-expansion of (13*E_4(z)^3 + 5*E_6(z)^2)/18. - Daniel D. Briggs, Nov 25 2011