CAPS 1995 Problem 1

Let $a_1=2, a_2=5$ and $a_{n+2}=(2-n^2)a_{n+1}+ (2+n^2)a_n$ for $n\geq 1$ . Do there exist $p,q,r$ so that $a_pa_q =a_r$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.