How can I get a closed formula for this expression?
$$n^{n-1}\left(1+\sum_{i=2}^{n} {\frac{2^{i-1}\cdot n!}{i^{i-1}}}\right)$$
I tried to split the sum into
$$\sum_{i=2}^{n} n!=(n-1)\cdot n!$$
and
$$\sum_{i=2}^{n} {\frac{2^{i-1}}{i^{i-1}}} = \sum_{i=2}^{n} {\left(\frac{2}i\right)^{i-1}}$$
but I still can not solve it. Any Ideas?