Limit of sequence. with Factorial

Can't find the limit of this sequence :

$$\frac{3^n(2n)!}{n!(2n)^n}$$ tried to solve this using the ratio test buy failed... need little help

Answer

What's the problem with the ratio test?:

$$\frac{a_{n+1}}{a_n}=\frac{(2n+2)!\color{red}{3^{n+1}}}{(n+1)!(\color{green}{2}(n+1))^{n+1}}\frac{n!(\color{green}{2}n)^n}{(2n)!\color{red}{3^n}}=\frac{(2n+1)\cdot3}{n+1}\left(\frac{n}{n+1}\right)^n\xrightarrow[n\to\infty]{}\frac6e>1$$

and thus...