Let \(\{U_n\}_{n\ge 0}\) and \(\{V_n\}_{n\ge 0}\) denote the sequence of ordinary ménage numbers and the sequence of straight ménage numbers respectively. In this paper, we mainly study the log-behavior of \(\{U_n\}_{n\ge 3}\) and \(\{V_n\}_{n\ge 2}\). We prove that \(\{U_n\}_{n\ge 6}\) and \(\{V_n\}_{n\ge 6}\) are log-balanced. In addition, we discuss the log-behavior of some sequences involving \(U_n\) (\(V_n\)).

中文翻译：

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Ménage 数字的对数行为

令\(\{U_n\}_{n\ge 0}\)和\(\{V_n\}_{n\ge 0}\)分别表示普通门数序列和直门数序列。在本文中，我们主要研究\(\{U_n\}_{n\ge 3}\)和\(\{V_n\}_{n\ge 2}\) 的对数行为。我们证明\(\{U_n\}_{n\ge 6}\)和\(\{V_n\}_{n\ge 6}\)是对数平衡的。此外，我们讨论了一些涉及\(U_n\) ( \(V_n\) ) 的序列的对数行为。