permutation transform?

[Peter Cameron]

On Thu, Sep 16, 2004 at 08:25:26PM -0500, Ross La Haye wrote:
> 
> Recently, I've become interested in the binomial transforms of integer
> sequences and today at work I was wondering if a similar transform has been
> defined that I'll call the permutation transform, and, if not, if it's
> interesting.  Simply, the transform (and its inverse) would be the same as
> with the binomial except that C(n,k) = n! / k!(n-k)! would be replaced with
> P(n,k) = n! / (n-k)!.  So for instance, for
> 
I notice that the permutation transform of a sequence (a_n) is the binomial
transform of (n! a_n).

Peter Cameron.