Fun combinatorics question: What's the number of valley-shaped arrays with the numbers 1 to n?
An array is valley-shaped if it is first decreasing and then increasing. Examples of valley-shaped arrays:
5, 3, 1, 2, 4
2, 1, 3, 4, 5
1, 2, 3, 4, 5
5, 4, 3, 2, 1