Time complexity of $T(n) = nT(n-1) + n^2$
We can compute the limit explicitly:
$$
1 + \sum_{n=0}^\infty \frac{n+1}{n!} = 1 + \sum_{n=0}^\infty \frac{1}{n!} + \sum_{n=1}^\infty \frac{1}{(n-1)!} = 2e + 1.
$$