Limit as n goes to infinity for $$\lim\_{n \to \infty}\frac{(n^2)!}{(2n)!}$$.

In my approach, I break down the numerator as 

$${(n^2)(n^2-1)...(2n+1)(2n)!}$$ 

and therefore the value of the original fraction would be infinity. But when I check with wolframalfa, i get the answer as zero. Where am I going wrong here?

Edit: Some comments have suggested that the parentheses in the numerator might not be correct. This is indeed the case.
-Thank you