$ \sqrt[n]{ \binom{n}{1} \cdot \binom{n}{2} \cdot \binom{n}{2} ........... \binom{n}{n} }$

Question

As a part of a limit question I was evaluating, it was required that I evaluate this sum. However I do know no easy closed forms of this.

I have tried applying the vandermonde identity but what is messing me up is the index of summation:

i.e:

$$ \sqrt[n]{ \binom{n}{1} \cdot \binom{n}{2} \cdot \binom{n}{2} ... \binom{n}{n} } = \sqrt[n]{ \sum_{k=0}^{?} \binom{n}{k} \binom{n}{n-k} }$$

So, my problem is with finding '?' which is the top of the index of sum.