Answer
Not monotonic, but bounded
Work Step by Step
Because the sequence isn’t always decreasing or increasing, it’s not monotonic.
To find if it is bounded. Find $\lim\limits_{n \to \infty} n e^{-\frac{n}{2}}$
From both intuition and the graph of the function it is clear that $ \frac{2}{e} \geq a_n \geq 0$. Because the maximum of $\frac{2}{e}$ is the upper bound and 0 is the lower bound as n goes to $\infty$
