Solving the recursion $F(n)=K_0F(n-1)/(n-1)+K_1F(n-2)/(n-2)$

Question

Please help me in solving the recursion $F(n)=K_0\frac{F(n-1)}{n-1}+K_1\frac{F(n-2)}{n-2}$, preferably using power series for the values of $F(n)$ in terms of $n$. Here $K_1$ and $K_2$ are constants. We are given $F(0)=0,F(1)=3,F(2)=3/2$. Any methods of solution is welcome, even partial answers. We can discuss further. Thanks for taking time to read my question.