Find closed formula for the recurrence $a_{n}=na_{n-1}+n(n-1)a_{n-2}$

Question

$a_{n}=na_{n-1}+n(n-1)a_{n-2}$ where a0 = 0, a1=1, and n >= 2.

I found an exponential generating function for this recurrence, but cant seem to find the closed form because the generating function doesn't look nice. How would i go aout finding the closed form for this? Thanks

Answer 1

Hint: Let $a_n=n!b_n$. The $b_n$ satisfy a familiar recurrence.