Really a fantastic polynomial problem

Algebra Level 5

Let P(x)P(x) be a nonzero polynomial such that (x1)P(x+1)=(x+2)P(x)(x-1)P(x+1) = (x+2)P(x) for every real xx, and (P(2))2=P(3)\left(P(2)\right)^2 = P(3). Then find P(2016)P(2016).

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