If $A=\lim_{n\to\infty}\bigg(\prod_{k=0}^{n} {n\choose k}\bigg) ^{\frac{1}{n(n+1)}}$. Then Find $A$

Question

If $$A=\lim_{n\to\infty}\bigg(\prod_{k=0}^{n} {n\choose k}\bigg) ^{\frac{1}{n(n+1)}}$$. Then Find $A$

My Approach:

$\prod_{k=0}^{n} {n\choose k}=\prod_{k=0}^{n}\dfrac{n!}{k!(n-k)!}=\dfrac{(n!)^{n+1}}{\bigg(0!\cdot1!\cdot2!.....(n)!\bigg)^2}$.

Now I don't Know how to proceed further. This question was given to a High School Students in some paper.