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

1,2

Links

Table of n, a(n) for n=1..45.

Formula

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

Example

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

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

Crossrefs

Row sums give: A000312.

Column k=1 and main diagonal give: A000142.

Sequence in context: A142471 A323233 A071208 * A216242 A330798 A260687

Adjacent sequences: A231533 A231534 A231535 * A231537 A231538 A231539

Keyword

nonn,tabl

Author

Geoffrey Critzer, Nov 10 2013

Status

approved