How to solve this recurrence of a sequence?

Question

$x_1=1$, $x_2=2$, $x_n=n\cdot x_{n-1}+\frac{n(n-1)}{2}x_{n-2}$

Thanks to Barry Cipra's suggestion, now I have obtained the solution for $x_n$:

$x_n=\frac{n!}{\sqrt{3}}((\frac{1+\sqrt{3}}{2})^n-(\frac{1-\sqrt{3}}{2})^n)$

Answer 1

Hint: Let $u_n=x_n/n!$. Find (and solve) a recurrence relation for $u_n$.