A231536 Triangular array read by rows. T(n,k) is the number of functions f:{1,2,...,n}->{1,2,...,n} whose functional digraph has exactly k nodes such that no nonrecurrent element is mapped into it. n >= 1, 1 <= k <= n.

1, 2, 2, 6, 15, 6, 24, 108, 100, 24, 120, 840, 1340, 705, 120, 720, 7200, 17400, 15150, 5466, 720, 5040, 68040, 231000, 296100, 171402, 46921, 5040, 40320, 705600, 3198720, 5644800, 4687536, 2015272, 444648, 40320, 362880, 7983360, 46569600, 108168480, 121144464, 73191888, 25011576, 4625361, 362880

Offset: 1

Author

Geoffrey Critzer, Nov 10 2013

Keywords

• nonn
• tabl

Examples

			T(3,3) = 6 because we have: (1,2,3),(2,1,3),(3,2,1),(1,3,2),(2,3,1),(3,1,2).  In these 6 functions represented as a word there are 3 (all) elements with zero nonrecurrent elements mapped to them.
1,
2, 2,
6, 15, 6,
24, 108, 100, 24,
120, 840, 1340, 705, 120,
720, 7200, 17400, 15150, 5466, 720
		

Crossrefs

Row sums give: A000312.

Column k=1 and main diagonal give: A000142.

Programs

Mathematica

nn=6;Map[Select[#,#>0&]&,Drop[Range[0,nn]!CoefficientList[Series[1/(1- (-x+x y-ProductLog[-Exp[x (-1+y)] x])),{x,0,nn}],{x,y}],1]]//Grid

Formula

E.g.f.: 1/(1 - A(x,y)) where A(x,y) is the e.g.f. for A055302.