TW-TST 1992 Problem 4

For a positive integer number $r$ , the sequence $a_{1},a_{2},...$ defined by $a_{1}=1$ and $a_{n+1}=\frac{na_{n}+2(n+1)^{2r}}{n+2}\forall n\geq 1$ . Prove that each $a_{n}$ is positive integer number, and find $n's$ for which $a_{n}$ is even.