Monotonicity of the sequence $\frac{(n/e)^n}{n!}$ When I draw the discrete function $f:\mathbb{N}_1\rightarrow[0,\infty)$ that is defined as follows
$$
f(n) := \frac{(n/e)^n}{n!}
$$
using Wolfram Alpha, the graph is descendant. Is it true that $f$ is non-increasing? Strictly decreasing? If so, how can this be proved? I tried investigating the behavior of the sequence $f(n+1)/f(n)$, however it converges to $1$, so this was no help.

Hint: $$\frac{f(n+1)}{f(n)} = \frac{((n+1)/e)^{n+1}}{(n+1)!}\frac{n!}{(n/e)^n}$$
Use that $(1 + \frac{1}{n})^n < e$.
