A008700 Theta series of Niemeier lattice of type D_4^6.

1, 144, 193104, 16809408, 397822032, 4630076640, 34416785088, 187487524224, 814891939920, 2975535123408, 9486534607200, 27053022904128, 70486183583424, 169931012132448, 384163644219264, 820166796086400

Offset

0,2

Comments

Also the theta series of the Niemeier lattice of type A_5^4 D_4. - clarified by Ben Mares, Jul 17 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 (2*E_4(z)^3 + E_6(z)^2)/3. - 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[ (2/3)*E4^3 + (1/3)*E6^2 + O[q]^terms, q] (* Jean-François Alcover, Jul 05 2017 *)

Crossrefs

Cf. A004009, A013973.

Cf. A008688 - A008699, A008701, A008702, A008703, A008704.

Sequence in context: A203098 A159724 A221124 * A047807 A023112 A159424

Adjacent sequences: A008697 A008698 A008699 * A008701 A008702 A008703

Keyword

nonn

Author

N. J. A. Sloane

Status

approved