|
%I #20 Mar 04 2020 13:52:59
%S 1,336,188496,16857792,397539408,4631004000,34415623872,187484309376,
%T 814908160080,2975513303952,9486512350560,27053125549632,
%U 70486112362176,169930901206752,384163721375616
%N Theta series of Niemeier lattice of type D_8^3.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H G. C. Greubel, <a href="/A008693/b008693.txt">Table of n, a(n) for n = 0..1000</a>
%F This series is the q-expansion of (7*E_4(z)^3 + 2*E_6(z)^2)/9. - _Daniel D. Briggs_, Nov 25 2011
%t 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 *)
%Y Cf. A004009, A013973.
%Y Cf. A008688 - A008692, A008694 - A008704.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
|
