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%I #9 May 10 2013 12:44:45
%S 1,1,3,18,157,1656,20727,300784,4955337,91229616,1853584651,
%T 41147256624,989990665677,25647894553048,711630284942319,
%U 21049888453838136,661180220075555473,21976354057916680416
%N E.g.f.: exp(x*exp(x*exp(x*exp(x))) + 1/3*x^3*exp(x*exp(x*exp(x)))^3).
%C a(n) is the number of functions f:{1,2,...,n} -> {1,2,...,n} such that the functional digraphs have cycles of length 1 or 3 and no element is at a distance of more than 3 from a cycle. - _Geoffrey Critzer_, Sep 23 2012
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
%F E.g.f.: exp(Sum_{d|m} T_k^d/d), where T_k = x*exp(T_(k - 1)), k >= 1, T_0 = x; k = 3, m = 3.
%t nn=20; a=x Exp[x]; b=x Exp[a]; c=x Exp[b]; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0,nn]! CoefficientList[Series[Exp[c+c^3/3], {x, 0, nn}], x] (* _Geoffrey Critzer_, Sep 23 2012 *)
%Y Cf. A000949-A000951, A060905-A060913.
%K nonn
%O 0,3
%A _Vladeta Jovovic_, Apr 07 2001
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