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%I #30 Sep 11 2022 09:33:40
%S 1,144,193104,16809408,397822032,4630076640,34416785088,187487524224,
%T 814891939920,2975535123408,9486534607200,27053022904128,
%U 70486183583424,169931012132448,384163644219264,820166796086400
%N Theta series of Niemeier lattice of type D_4^6.
%C Also the theta series of the Niemeier lattice of type A_5^4 D_4. - clarified by _Ben Mares_, Jul 17 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="/A008700/b008700.txt">Table of n, a(n) for n = 0..1000</a>
%F This series is the q-expansion of (2*E_4(z)^3 + E_6(z)^2)/3. - _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[ (2/3)*E4^3 + (1/3)*E6^2 + O[q]^terms, q] (* _Jean-François Alcover_, Jul 05 2017 *)
%Y Cf. A004009, A013973.
%Y Cf. A008688 - A008699, A008701, A008702, A008703, A008704.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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