How do I solve $A_{n+2}-3A_{n+1}+A_{n}=n$ with $A_{0}=A_{1}=1$ using method of generating function?

Question

$A_{n+2}-3A_{n+1}+A_{n}=n$ with $A_{0}=A_{1}=1$ using method of generating function

I deducted the following formula: $$ F(x)= \frac{x^3}{(x-1)(2x-1)}-\frac{1}{x-1} \;, $$ where $F(x)= \sum_{n=0}^{\infty} A_n x^n$, from here I don't know how to continue.