Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be a positive integer. A sequence of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
positive integers (not necessarily distinct) is called full if it satisfies the following condition: for each positive integer
![k\geq2](/media/m/6/9/c/69c4170fa46a91b6265eb781bcaf2f6c.png)
, if the number
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
appears in the sequence then so does the number
![k-1](/media/m/e/2/5/e2582f1a41d7cbbc089069312ee7488a.png)
, and moreover the first occurrence of
![k-1](/media/m/e/2/5/e2582f1a41d7cbbc089069312ee7488a.png)
comes before the last occurrence of
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
. For each
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
, how many full sequences are there ?
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Let $n$ be a positive integer. A sequence of $n$ positive integers (not necessarily distinct) is called full if it satisfies the following condition: for each positive integer $k\geq2$, if the number $k$ appears in the sequence then so does the number $k-1$, and moreover the first occurrence of $k-1$ comes before the last occurrence of $k$. For each $n$, how many full sequences are there ?