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%I #8 May 21 2012 15:25:28
%S 1,1,4,27,244,2745,36966,580111,10399096,209672721,4696872490,
%T 115732052271,3110867569140,90587751885241,2840805169411678,
%U 95450112571474095,3420897993621996016,130266500391456691233,5252293203395848789842,223535386151669737094095,10014286301754519472897900
%N Number of functions f:{1,2,...,n}->{1,2,...,n} such that every non-recurrent element has at most one preimage.
%C An element x of {1,2,...,n} is a recurrent element if there exists a positive integer k such that (f^k)(x) = x where f^k is the k-th iteration of functional composition.
%C The functional digraphs are composed of cycles of rooted trees with every non-root vertex of degree 1 or 2. Cf. A006152.
%F E.g.f.: 1/(1-A(x)) where A(x) is the e.g.f. for A006152.
%t nn=20;a=x Exp[x/(1-x)];Range[0,nn]! CoefficientList[Series[1/(1-a),{x,0,nn}],x]
%K nonn
%O 0,3
%A _Geoffrey Critzer_, May 21 2012
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