Let $a\in (0, 1)$ and and $n\in\mathbb N, n\ge 2$.
I would like to find a positive constant $k$ depending only on $n$ such that $$(\Gamma(n))^{-a/n} \ge k,$$
where $\Gamma$ denotes the Gamma function: https://en.wikipedia.org/wiki/Gamma_function.
Anyone could help with that?
I have observed that $a/n < 1/n$ and $\Gamma(n)\ge 1$, but anyway I am not able to find a $k$ satisfying that inequality.