MathDB

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 ?

Problem Statement