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%I #19 Jul 24 2021 02:24:31
%S 1,0,0,0,18,0,0,0,144,512,0,0,672,0,0,0,2034,4608,0,0,4320,0,0,0,7392,
%T 18432,0,0,12672,0,0,0,22608,47616,0,0,34802,0,0,0,44640,101376,0,0,
%U 60768,0,0,0,93984,193536,0,0,125280,0,0,0,141120,324096,0,0
%N Theta series of {D_9}* lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.
%H Andy Huchala, <a href="/A008424/b008424.txt">Table of n, a(n) for n = 0..3000</a>
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Ds9.html">Home page for this lattice</a>
%F Theta series in terms of Jacobi theta series: (theta_2)^9 + (theta_3)^9. - _Sean A. Irvine_, Mar 28 2018
%e G.f. = 1 + 18*q^4 + 144*q^8 + ...
%o (PARI)
%o N=66; q='q+O('q^N);
%o T3(q) = eta(q^2)^5 / ( eta(q)^2 * eta(q^4)^2 );
%o T2(q) = eta(q^4)^2 / eta(q^2);
%o Vec( T3(q^4)^9 + (2 * q * T2(q^4))^9 )
%o \\ _Joerg Arndt_, Mar 29 2018
%o (Magma)
%o L := Dual(Lattice("D", 9));
%o B := Basis(ThetaSeriesModularFormSpace(L), 100);
%o S := [ 1, 0, 0, 0, 18];
%o Coefficients(&+[B[i] * S[i] : i in [1..5]]); // _Andy Huchala_, Jul 24 2021
%Y Cf. A008431.
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_
%E More terms from _Andy Huchala_, Jul 24 2021
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