IMC 2019 · Problem 4

Define the sequence $a_0, a_1, \ldots$ of numbers by the following recurrence:

$$a_0 = 1, \quad a_1 = 2, \quad (n + 3)a_{n+2} = (6n + 9)a_{n+1} - na_n \quad \text{for } n \ge 0.$$

Prove that all terms of this sequence are integers.