Let $\Gamma$ be the analytic continuation of the Gamma function $$\Gamma:z\mapsto \int_0^{+\infty} x^{z-1}e^{-x}dx$$ on the complex plane except non-positive integers.
We know that $\Gamma$ has no zeros but simple poles on $\{0,-1,-2,-3,\ldots\}$. So if we define $G:z\mapsto \dfrac{1}{\Gamma(z)}$, this is an entire function with only simple zeros at $\{0,-1,-2,-3,\ldots\}$.
My questions are the followings:
What is the behavior between two zeros of $G$ ? What is the growth of $G$ in $[-(n+1),-n]$? Do we know if, for example, $\displaystyle \dfrac{e^{- t^2}}{\Gamma(t)} \underset{t\to -\infty}{\longrightarrow} 0$ ?