MathNet 2026 — Part 04 Question 185

How many sequences $a_1, a_2, \dots, a_{2008}$ are there such that each of the numbers $1, 2, \dots, 2008$ occurs once in the sequence, and $i \in \{a_1, a_2, \dots, a_i\}$ for each $i$ such that $2 \le i \le 2008$?