Permutations with fixed points

[Rob Pratt]

It seems you left out the identity permutation, which has n fixed points.

http://www.research.att.com/~njas/sequences/A002467

The game of Mousetrap with n cards (given n letters and n envelopes, how many ways are there to fill the envelopes so that at least one letter goes into its right envelope?).

0, 1, 1, 4, 15, 76, 455, 3186, 25487, 229384

-----Original Message-----
From: zak seidov [mailto:zakseidov at yahoo.com]
Sent: Friday, January 04, 2008 11:05 AM
To: seqfan at ext.jussieu.fr
Subject: Permutations with fixed points

Dear seqfans,
what is wrong with this sequence?
why is not it in OEIS?
thanks, zak

0,3,14,75,454,3185,25485,229382
Number of permutations of set {1..n} with at least one
fixed point, n>=2.
a(3)=3 because there are three permutations  with at
least one fixed point
with {1,2,3}:
{1,3,2},{2,1,3},{3,1,2};
a(4)=14 because there are 14 permutations  with at
least one fixed point
with {1,2,3,4}:
{1,2,4,3},{1,3,2,4},{1,3,4,2},{1,4,2,3},{1,4,3,2},{2,1,3,4},{2,3,1,4},{2,4,3,1},{3,1,2,4},{3,2,1,4},{3,2,4,1},{4,1,3,2},{4,2,1,3},{4,2,3,1}


--- superseq-reply at research.att.com wrote:

> Date: Fri, 4 Jan 2008 10:53:31 -0500 (EST)
> From: superseq-reply at research.att.com
> To: zakseidov at yahoo.com
> Subject: Reply from superseeker
>
> Report on [ 14,75,454,3185,25485,229382]:
> Many tests are carried out, but only potentially
> useful information
> (if any) is reported here.
>
>
> Even though there are a large number of sequences in
> the table, at least
> one of yours is not there! Please send it to me
> using
> the submission form on the sequence web page
>
http://www.research.att.com/~njas/sequences/Submit.html
> and I will (probably) add it!  Include a brief
> description. Thanks!
>
> o  Take a look at my web page which does lookups
> "online"!  Go to:
>       http://www.research.att.com/~njas/sequences/
> o  The whole sequence table is also visible there,
> as well as
>      an explanation of the symbols used in the
> table.
> o  If the sequence you looked up was not in the
> table,
>      please send it to me using the submission form
> on the web page!
> o  The server  sequences at research.att.com  does a
> simple lookup in the
>    On-Line Encyclopedia of Integer Sequences
> o  If the word "lookup" does not appear you will be
> sent the help file.
>
> Sequentially yours, The On-Line Encyclopedia of
> Integer Sequences,
> N. J. A. Sloane, AT&T Research, Florham Park NJ
> 07932-0971 USA njas at research.att.com
>



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