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.
1, 0, 1, 2, 0, 2, 3, 12, 0, 6, 28, 24, 72, 0, 24, 125, 400, 180, 480, 0, 120, 1146, 2220, 4680, 1440, 3600, 0, 720, 8827, 29064, 30870, 53760, 12600, 30240, 0, 5040, 94200, 272272, 545328, 409920, 638400, 120960, 282240, 0, 40320, 1007001, 3722688, 5989032, 9386496, 5518800, 7983360, 1270080, 2903040, 0, 362880
Offset: 0
Examples
1, 0, 1, 2, 0, 2, 3, 12, 0, 6, 28, 24, 72, 0, 24, 125, 400, 180, 480, 0, 120, 0 1146, 2220, 4680, 1440, 3600, 0, 720
Crossrefs
Cf. A006153.
Programs
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Mathematica
nn=6;a=x Exp[x];Range[0,nn]!CoefficientList[Series[1/(1-x (Exp[x]-1+y)),{x,0,nn}],{x,y}]//Grid
Formula
E.g.f.: 1/(1 - x*(exp(x) -1 + y)).
Comments