login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A090657 Triangle read by rows: T(n,k) = number of functions from [1,2,...,n] to [1,2,...,n] such that the image contains exactly k elements (0<=k<=n). 10
1, 0, 1, 0, 2, 2, 0, 3, 18, 6, 0, 4, 84, 144, 24, 0, 5, 300, 1500, 1200, 120, 0, 6, 930, 10800, 23400, 10800, 720, 0, 7, 2646, 63210, 294000, 352800, 105840, 5040, 0, 8, 7112, 324576, 2857680, 7056000, 5362560, 1128960, 40320 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Another version is in A101817. - Philippe Deléham, Feb 16 2013

LINKS

Alois P. Heinz, Rows n = 0..62, flattened

FORMULA

T(n,k) = C(n,k) * k! * A048993(n,k).

T(n,k) = A008279(n,k) * A048993(n,k).

T(n,k) = C(n,k) * A019538(n, k).

T(n,k) = C(n,k) * Sum_{j=0..k} (-1)^(k-j) * C(k,j) * j^n.

T(n,k) = n * (T(n-1,k-1) + k/(n-k) * T(n-1,k)) with T(n,n) = n! and T(n,0) = 0 for n>0.

EXAMPLE

Triangle begins:

1;

0,  1;

0,  2,   2;

0,  3,  18,   6;

0,  4,  84, 144, 24;

MAPLE

T:= proc(n, k) option remember;

      if k=n then n!

    elif k=0 or k>n then 0

    else n * (T(n-1, k-1) + k/(n-k) * T(n-1, k))

      fi

    end:

seq (seq (T(n, k), k=0..n), n=0..10);

MATHEMATICA

Table[Table[StirlingS2[n, k] Binomial[n, k] k!, {k, 0, n}], {n, 0, 10}] // Flatten  (* Geoffrey Critzer, Sep 09 2011 *)

CROSSREFS

Row sums give: A000312. Columns k=0-2 give: A000007, A001477, A068605. Diagonal, lower diagonal give: A000142, A001804. Cf. A007318, A048993, A019538, A008279.

Cf. A101817.

Sequence in context: A011137 A143396 A244129 * A167001 A108563 A138476

Adjacent sequences:  A090654 A090655 A090656 * A090658 A090659 A090660

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Dec 14 2003

EXTENSIONS

Revised description from Jan Maciak, Apr 25 2004

Edited by Alois P. Heinz, Jan 17 2011

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 24 10:51 EST 2014. Contains 249895 sequences.