Talk:Derangement

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d(n) also satisfies the recurrence: d(n) = n*d(n-1) + (-1)^n.
see: http://mathworld.wolfram.com/Derangement.html
I've seen the relation proved by inclusion-exclusion.
DonkeyKong the mathematician (in training) 08:19, 17 July 2006 (UTC)

[edit] General formula

The page about rencontres numbers gives a general formula for the derangements as the closest integer to n! \over e. Is this formula valid for all n? I checked with the first points (ok), and it's obviously valid in the limit. Is there a proof? A corollary of this formula would be a proof that e is irrational. Albmont 13:24, 14 November 2006 (UTC)

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