A008693 Theta series of Niemeier lattice of type D_8^3.

1, 336, 188496, 16857792, 397539408, 4631004000, 34415623872, 187484309376, 814908160080, 2975513303952, 9486512350560, 27053125549632, 70486112362176, 169930901206752, 384163721375616

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 (7*E_4(z)^3 + 2*E_6(z)^2)/9. - 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[(7/9)*E4^3 + (2/9)*E6^2 + O[q]^terms, q] (* Jean-François Alcover, Jul 05 2017 *)

Crossrefs

Cf. A004009, A013973.

Cf. A008688 - A008692, A008694 - A008704.

Sequence in context: A268969 A056933 A289346 * A068298 A003790 A003924

Adjacent sequences: A008690 A008691 A008692 * A008694 A008695 A008696

Keyword

nonn

Author

N. J. A. Sloane

Status

approved