recontre (sub-factorial or derangement) numbers

[Max]

On 3/4/06, wouter meeussen <wouter.meeussen at pandora.be> wrote:
> A000166 they are. Round[n! / E ], or !n for short.
> Counts permutations without fixed points.
>
> Now look at the GCD of n! and !n.
> {1,1,2,3,4,5,18,7,8,81,10,11,36,13,14,495,16,17,486,209,260,63, ..
> it is different from (n-1) only
> for n= {1,7,10,13,16,19,20,21,22,23,25,27,28,31,34..
> why so?

Why not? What is special about that numbers?

> Why is Mod[n! , !n] equal to n!-2*!n (that's A055596) for n>3 ?

Because 2*!n < n! < 3*!n.

Max