  Several continued fraction expansions for $e$ have been produced by an
automated conjecture generator (ACG) called \emph{The Ramanujan Machine}. Some
of these were already known, some have recently been proved and some remain
unproven. While an ACG can produce interesting putative results, it gives very
limited insight into their significance. In this paper, we derive an elegant
continued fraction expansion, equivalent to a result from the Ramanujan
Machine, using the sequence of ratios of factorials to subfactorials or
derangement numbers.
