# Is inverse of a combination function negligible?

Can anyone help me in determining whether $1/{n\choose a}$ negligible function for sufficiently large value of $n$, say for example $n=p^2$ and $a=p$, for an integer $p$?

$$1/{n\choose a}=\frac{a!(n-a)!}{n!}=\frac{p!(p^2-p)!}{(p^2)!}=\frac{p!(p^2)!}{(p^2)!\prod^{p-1}_{i=1}(p^2-i)}=\frac{p!}{\prod^{p-1}_{i=0}(p^2-i)}$$