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%I #30 Sep 14 2022 08:25:53
%S 1,240,190800,16833600,397680720,4630540320,34416204480,187485916800,
%T 814900050000,2975524213680,9486523478880,27053074226880,
%U 70486147972800,169930956669600,384163682797440,820166912933760
%N Theta series of Niemeier lattice of type D_6^4.
%C Also the theta series for the Niemeier lattice of type A_9^2 D_6. - clarified by _Ben Mares_, Sep 13 2022
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H G. C. Greubel, <a href="/A008696/b008696.txt">Table of n, a(n) for n = 0..1000</a>
%F This series is the q-expansion of (13*E_4(z)^3 + 5*E_6(z)^2)/18. - _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[ (13/18)*E4^3 + (5/18)*E6^2 + O[q]^terms, q] (* _Jean-François Alcover_, Jul 05 2017 *)
%Y Cf. A004009, A013973.
%Y Cf. A008688 - A008695, A008697 - A008704.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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