Let $Z \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number.
Let $n \in \mathbb{N}$ be a D996: Natural number.
Let $n \in \mathbb{N}$ be a D996: Natural number.
Then
\begin{equation}
\mathbb{E}(Z^n)
=
\begin{cases}
(n - 1) !!, \quad & n \in 2 \mathbb{N} \\
0, \quad & n \in 2 \mathbb{N} + 1
\end{cases}
\end{equation}