During my study, I ended up with the following distribution below. Is this a variant of a known distribution type? It is over semi-bounded support.
\begin{equation} p(X=x) = \frac{e^{-\frac{x^2}{2}}\left(e^{\frac{x^2}{2}}-1\right)}{x^2} \end{equation}
I have tried to match it to several distributions but to no avail.
Thanks!