[Math] Asymptotic for binomial coefficient with square root

Question

I'm looking for asymptotic estimate for the binomial coefficient:
$$
\ln{\binom{n}{[\sqrt{n}]}}
$$
I assume Stirling's approximation can help, but I'm not sure I will get any good estimation with this approach. Is there any good way to make an estimation for this coefficient? Thanks in advance.

Answer 1

Using Shitikanth's hint I think you're going to be coming up with $$\text{ln}{n \choose [\sqrt{n}]}\approx\text{ln}\left(\frac{n^{n+\sqrt{n}/2+3/4}}{\left(n-\sqrt{n}\right)^{1/2-\sqrt{n}+n}}\right).$$