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%I #19 May 30 2022 12:29:41
%S 1,144,8784,294336,5883984,71916768,547468992,2882049408,12927121488,
%T 45761350608,150532923744,416276152128,1118182645440,2614241349216,
%U 6094718050176,12618123283584,26478496036944
%N Theta series of direct sum of 6 copies of D_4 lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 119.
%H Seiichi Manyama, <a href="/A008662/b008662.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Da#D4">Index entries for sequences related to D_4 lattice</a>
%e G.f. = 1 + 144*q + 8784*q^2 + 294336*q^3 + 5883984*q^4 + 71916768*q^5 + ... - _Michael Somos_, May 27 2022
%t terms = 17; s = (1/2 (EllipticTheta[3, 0, q]^4 + EllipticTheta[4, 0, q]^4) )^6 + O[q]^(2 terms); CoefficientList[s, q^2] (* _Jean-François Alcover_, Jul 08 2017 *)
%t a[ n_] := With[{e1 = q*QPochhammer[q]^24, e2 = q^2*QPochhammer[q^2]^24}, SeriesCoefficient[(e1 + 64* e2)^3 / (e1* e2), {q, 0, n}]]; (* _Michael Somos_, May 27 2022 *)
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_