Let P(x) be a nonzero polynomial such that (x-1)P(x+1) = (x+2)P(x) for every real x, and P(2)^2 = P(3). Then find P(2016).
Entering (2,4),(3,16),(4,40),(5,80), evaluated from the text, into a linear equation solver we get
p(x)=2/3*(x^3-x) as a direct formula
evaluating p(2016) we get 5,462,358,720