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%I #7 Mar 30 2012 18:39:17
%S 0,1,2,6,24,116,625,3580,21297,130084,810737,5135142,32961216,
%T 213940962,1401821021,9260154974,61603278951,412352572116,
%U 2775230479959,18768654394542,127482450424964,869287197637752,5948547336578541
%N Enumeration of fractal 321 avoiders.
%C See page 12-15 of link.
%H M. H. Albert, <a href="http://www.cs.otago.ac.nz/trseries/oucs-2002-11ver2.pdf">The fine structure of 321 avoiding permutations</a>.
%F G.f. A(x) satisfies A(x)^6+(-2*x+3)*A(x)^4+(-2*x-1)*A(x)^3+(x^2-3*x+3)*A(x)^2+(2*x^2-2*x-1)*A(x)+x^2+x=0; a(n+1)/a(n) ->7.346751...
%o (PARI) a(n)=local(A); if(n<1,0,A=x+O(x^2); for(m=2,n,A=Pol(A)+x*O(x^m); A=A^6+(-2*x+3)*A^4+(-2*x-1)*A^3+(x^2-3*x+3)*A^2+(2*x^2-2*x)*A+x^2+x); polcoeff(A,n))
%K nonn
%O 0,3
%A _Benoit Cloitre_, May 24 2003