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%I A219530 #6 Nov 24 2012 21:25:36
%S A219530 1,1,4,24,195,2046,26752,422546,7849611,167781117,4054557471,
%T A219530 109246333917,3245641491658,105366022410057,3709933487122164,
%U A219530 140791348680766521,5728108758307500165,248696925989154108462,11476424805495560002162,560894026563924188981599,28941826672247857117927894
%N A219530 Number of functions f:{1,2,...,n}->{1,2,...,n} such that each component of f is a function on an interval of {1,2,...,n}.
%C A219530 Here, a component of f is a weakly connected component of its functional digraph.
%F A219530 G.f.: 1/ (1 - A(x)) where A(x) is the o.g.f. for A001865.
%e A219530 a(3)=24 because there are 27 functions f:{1,2,3}->{1,2,3} but three of these are not counted: 1->3 2->2 3->3; 1->3 2->2 3->1; 1->1 2->2 3->1.
%t A219530 nn=20; t= Sum[n^(n-1)x^n/n!, {n,1,nn}]; a=Range[0,nn]! CoefficientList[Series[Log[1/(1-t)], {x,0,nn}], x]; b=Sum[a[[i]]x^(i-1), {i,1,nn+1}]; CoefficientList[Series[1/(1-b), {x,0,nn}], x]
%K A219530 nonn
%O A219530 0,3
%A A219530 _Geoffrey Critzer_, Nov 21 2012

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