login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 14 13:43 EDT 2022. Contains 356117 sequences. (Running on oeis4.)