Question

proof of derangement without using recurrence?

Answer 1

You have a question about derangements?
I know (for example) that the number 123 has 2 derangements.

Answer 2

for example the 2 derangements of 123 are
231 and 312

Answer 3

i am looking for a proof of derangement formula D(n)=n!(1-1/1!+1/2!..)so on but without using recurrence

Answer 4

The reason I am curious is that I wrote a derangement calculator just about a month ago:
http://www.1728.org/derange.htm

Answer 5

I am searching for a proof of the derangement formula (which I assume you have done) without using recurrence of course.
At the moment I have found the "Inclusion–exclusion principle" article in Wikipedia.
http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle#Counting_derangements
If you have already researched this please let me know.