Example 1-26 $n$ couples sit around a round table, find the number of ways in which each couple sits next to each other.

 untranslated text:
例 1-26 $n$ 对夫妻围一圆桌而坐, 求每对夫妻相邻而坐的方案数. 

 translated text:
Example 1-26 $n$ couples sit around a round table, find the number of ways in which each couple sits next to each other.
A husband and wife sit next to each other but can swap positions, so the number of arrangements $N=(n-1)!\times 2^{n}$.