The problem I have is to solve the following recurrence relation :
$S(1) = 1$
$S(n) = \sum_{i=1}^{n-1} (i\cdot S(i))$
I figured out the solution is:
$S(n) = \frac{n!}{2}$
mostly by calculating the first few values for $n$ and trying to find patterns.
However, I would like to know if there is a more structured method(s) for finding the solution?
Thank you :)