On polynomial solutions of the Diophantine equation (x+y-1)^2 = wxy

In this paper we consider a particular class of polynomials arising from the solutions of the Diophantine equation (x+y−1)2 = wxy. We highlight some interesting aspects, describing their relationship with many iportant integer sequences and pointing out their connection with Dickson and Chebyshev polynomials. We also study their coefficients finding a new identity involving Catalan numbers and proving that they are a Riordan array.