A008695 Theta series of Niemeier lattice of type A_11 D_7 E_6.

1, 288, 189648, 16845696, 397610064, 4630772160, 34415914176, 187485113088, 814904105040, 2975518758816, 9486517914720, 27053099888256, 70486130167488, 169930928938176, 384163702086528

Offset

0,2

Comments

Also the theta series of the Niemeier lattice of type E_6^4. - 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

Formula

This series is the q-expansion of (3*E_4(z)^3 + E_6(z)^2)/4. - Daniel D. Briggs, Nov 25 2011

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[ (3/4)*E4^3 + (1/4)*E6^2 + O[q]^terms, q] (* Jean-François Alcover, Jul 05 2017 *)

Crossrefs

Cf. A004009, A013973.

Cf. A008688 - A008694, A008696 - A008704.

Sequence in context: A037946 A282102 A159299 * A047805 A173150 A282332

Adjacent sequences: A008692 A008693 A008694 * A008696 A008697 A008698

Keyword

nonn

Author

N. J. A. Sloane

Status

approved