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Omni-MATH / Let n be a positive integer. A sequence of n positive integers (not necessarily distinct) is called [b]full[/b] if it satisfies the following condition: for each positive integer …

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problem

Let nn be a positive integer. A sequence of nn positive integers (not necessarily distinct) is called [b]full[/b] if it satisfies the following condition: for each positive integer k≥2k\geq2, if the number kk appears in the sequence then so does the number k−1k-1, and moreover the first occurrence of k−1k-1 comes before the last occurrence of kk. For each nn, how many full sequences are there ?
Plain-text mathematical notation (without MathML)
Let n be a positive integer. A sequence of n positive integers (not necessarily distinct) is called [b]full[/b] if it satisfies the following condition: for each positive integer k≥2, 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 ?
Original LaTeX notation
Let $n$ be a positive integer. A sequence of $n$ positive integers (not necessarily distinct) is called [b]full[/b] 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 ?

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Source and history

task_id
31466b76-d0d2-5d22-8239-3e40e3aaf909
task_key
test--31466b76-d0d2-5d22-8239-3e40e3aaf909
task_revision_id
1
config / split
/ test

Official source

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