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%I #17 Jun 13 2019 04:15:18
%S 1,132,2970,19800,66462,194832,420684,881760,1511730,2770284,4134240,
%T 6754968,9491130,14310120,18773964,27609648,34253142,47864520,
%U 58862870,78974808,93470652,125490024,143483340,186539760,214957644,271553700,304365600
%N Theta series of A_11 lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110.
%H Vincenzo Librandi, <a href="/A023902/b023902.txt">Table of n, a(n) for n = 0..1000</a>
%t terms = 21; f[q_] = LatticeData["A11", "ThetaSeriesFunction"][-I Log[q] / Pi]; s = Series[f[q], {q, 0, 2 terms}]; CoefficientList[s, q^2][[1 ;; terms]] (* _Jean-François Alcover_, Jul 04 2017 *)
%o (PARI) theta3(k,n,prec,f,m)=f=polcyclo(n);1+sum(m=1,sqrtint(prec),Mod(x^(m*k%n)+x^(m*(n-k)%n),f)*q^sqr(m))+O(q^(prec+1))
%o aaa(n,prec,k,m)=sum(k=0,n-1, theta3(k,n,prec)^n)/n/(1+2*sum(m=1,sqrtint(floor(prec/n)),q^(n*sqr(m)))+O(q^(prec+1)))
%o doit(m,prec)=subst(lift(aaa(m+1,prec)),x,0) \\ gives theta series of A_m to order "prec"; code from Robert.Harley(AT)inria.fr
%K nonn
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Sean A. Irvine_, Jun 12 2019
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