$e$的秩和连分数
Derangements and Continued Fractions for $e$
摘要：
几个连分数展开$e$已产生的自动猜想生成器（ACG）称为\emph{The Ramanujan Machine}。其中一些是已知的，一些最近已被证明，还有一些尚未得到证实。虽然ACG可以产生有趣的推定结果，但它对它们的意义提供了非常有限的见解。在本文中，我们得到了一个优雅的连分数的扩展，相当于一个结果，从拉马努金机，使用的比例序列的因子，子因子或错位数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
