I found a similar problem on one of my problem sets and am struggling with how to approach the problem.
The problem is as follows: $$ \text{Evaluate} \sum _{k=1}^{n}\:P(n, k-1)P(n-1,n-k). $$
The function $P(n, r)$ represents the number of permutations of length $r$ you can form from $n$ total objects.
Using a Computer Solver (Sympy), I know that the answer is $(2^{n}-1)(n-1)!$. However, I am not sure how to get there. I would appreciate any insights into how to approach this problem and/or a walkthrough on how to get the solution.