As a generalization of second order recurrence sequences, the authors define the polynomials \[ A_{n+1}(x)=p(x)A_n(x)+q(x)A_{n-1}(x), \] with initial conditions \(A_0(x)=a(x)\) and \(A_1(x)=b(x)\), where \(a,b,p,q\) are given real polynomials.
Recurrences, tridiagonal determinantal matrix representations and factorizations are given.