Define a sequence $(u\_k)$ by 

$u\_0=0$,$u\_k=({k+2 \over k})u\_{k-1}+{1 \over k}$.

Find $u\_n$.

I couldn't get an idea on how to even start. But to help the community, the sequence goes like this starting from $u\_0$.

$0,1,2.5,4.5,7,10,13.5,17.5$

Thanks.