BALKAN 1990 Problem 1

The sequence $(a_{n})_{n\geq 1}$ is defined by $a_{1} = 1, a_{2} = 3$ , and $a_{n + 2} = (n + 3)a_{n + 1} - (n + 2)a_{n}, \forall n \in \mathbb{N}$ . Find all values of $n$ for which $a_{n}$ is divisible by $11$ .