Is there another way of expressing $\sum\limits_{k=1}^n \binom{n}{k} \cdot (n-k)! \cdot k!$?
I have stumbled across the formula $ \sum\limits_{k=1}^n \binom{n}{k} \cdot (n-k)! \cdot k!$ in some applied context. It looks as though there might be a nice combinatorial background to this formula. Is there another way to express it? Maybe a term that only depends on n? I am thinking of the famous equation expressing $ […]