Permutations with fixed points

[Tanya Khovanova]

You are right.

The statement in A000166:
 The termwise sum of this sequence and A003048 gives the factorial
numbers - D. G. Rogers, Aug 26 2006 
should be changed to refer to A002467

Also the statement in A003048:
 The termwise sum of this sequence and A000166 gives the factorial
numbers - D. G. Rogers, Aug 26 2006
Should be moved to the sequence A002467

Tanya

--- Martin Fuller <martin_n_fuller at btinternet.com> wrote:

> A000166 (permutations with no fixed points) contains the following
> formula:  "The termwise sum of this sequence and A003048 gives the
> factorial numbers".  A003048 has an equivalent formula.
> 
> I do not understand how that formula works.  Should it refer to
> A002467
> instead?
> 
> Martin Fuller
> 
> --- Tanya Khovanova <mathoflove-seqfan at yahoo.com> wrote:
> 
> > Your sequence is the sequence A002467 minus one, as you do not
> count
> > an
> > identical permutation.
> >  
> > Tanya
> > 
> > --- zak seidov <zakseidov at yahoo.com> wrote:
> > 
> > > 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
> > > > 
> > > 
> > > 
> > > 
> > >      
> > >
> >
>
____________________________________________________________________________________
> > > Never miss a thing.  Make Yahoo your home page. 
> > > http://www.yahoo.com/r/hs
> > > 
> > 
> > 
> 
>