You can't rewrite it as a single factorial, but an expression containing several:
[tex]4n^2+2n=2n(2n+1)=\dfrac{(2n+1)(2n)(2n-1)\cdots2\cdot1}{(2n-1)\cdots2\cdot1}=\dfrac{(2n+1)!}{(2n-1)!}[/tex]
