Good evening, I'm trying to find an asymptotic of this sum:

$$\sum_{j=0}^n (-1)^j {n \choose j} (n - j)^n = n^n - {n \choose 1} (n - 1)^n + {n \choose 2} (n - 2)^n + ... + (-1)^n {n \choose n} (n - n)^n $$

I think there is no close form. But I don't know how to calculate an asymptotics than. Maybe I should try to approximate it by some integral?

Thank you for any help!