Školjka

Dan je niz $a_1 = 1, a_2 = 1$ i $$ a_{n+1} = \frac{a_2^2}{a_1} + \frac{a_3^2}{a_2} + \dots + \frac{a_n^2}{a_{n-1}} \quad \text{za} \quad n \in \mathbb{N}, n \geq 2 \text{.} $$ Odredi $a_{2016}$.