Solve the recurrence

a

n

$=$

n

a

n

$$

$1$

$+$

n

$!$

a

n

$$

$=$na

n$1$

$$

$+$n$!$ for

n

$>$

$0$

n$>0$ with

a

$0$

$=$

$1$

a

$0$

$$

$=1.$ Give a simple expression for

a

n

a

n

$$

$.$