I just found that sum of \(n\) permutations with \(i\) equals \(e\Gamma(n+1, 1)\). In other words,

\(P(n,0) + P(n,1) + P(n, 2) + .... P(n,n) = e\Gamma(n+1, 1)\). [where \(\Gamma(x,y)\) is the incomplete gamma function].

Can anyone give a proof of this?

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TopNewestHi Kartik Sharma , see this or the solution to this question .

But if you aren't familiar with Gamma function , see the link I provided or see it here .

Hope I was useful !!!

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Thanks, that was helpful. You are quite good, solves almost all the problems.

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You are welcome.

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here too? *If only you have time.

Then, can you help meLog in to reply