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A220222 Triangular array read by rows. T(n,k) is the number of functional digraphs on {1,2,...,n} such that no node is at a distance greater than one from a cycle and there are k recurrent elements whose preimage contains only one element, n>=0, 0<=k<=n.

%I A220222 #12 Jan 17 2013 09:17:23
%S A220222 1,0,1,2,0,2,3,12,0,6,28,24,72,0,24,125,400,180,480,0,120,1146,2220,
%T A220222 4680,1440,3600,0,720,8827,29064,30870,53760,12600,30240,0,5040,94200,
%U A220222 272272,545328,409920,638400,120960,282240,0,40320,1007001,3722688,5989032,9386496,5518800,7983360,1270080,2903040,0,362880
%N A220222 Triangular array read by rows. T(n,k) is the number of functional digraphs on {1,2,...,n} such that no node is at a distance greater than one from a cycle and there are k recurrent elements whose preimage contains only one element, n>=0, 0<=k<=n.
%C A220222 Row sums =  A006153. Column for k=0 is A052848.
%F A220222 E.g.f.: 1/(1 - x*(exp(x) -1 + y)).
%e A220222 1,
%e A220222 0,    1,
%e A220222 2,    0,    2,
%e A220222 3,    12,   0,    6,
%e A220222 28,   24,   72,   0,    24,
%e A220222 125,  400,  180,  480,  0,    120, 0
%e A220222 1146, 2220, 4680, 1440, 3600, 0,   720
%t A220222 nn=6;a=x Exp[x];Range[0,nn]!CoefficientList[Series[1/(1-x (Exp[x]-1+y)),{x,0,nn}],{x,y}]//Grid
%Y A220222 Cf. A006153.
%K A220222 nonn,tabl
%O A220222 0,4
%A A220222 _Geoffrey Critzer_, Dec 07 2012