A231536 - OEIS

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

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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.

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