Let K be a field and put {mathcal {A}}:={(i,j,k,m)in mathbb {N}^{4}:;ile j;text{ and };mle k}. For any given Ain {mathcal {A}} we consider the sequence of polynomials (r_{A,n}(x))_{nin mathbb {N}} defined by the recurrence rA,n(x)=fn(x)rA,n-1(x)-vnxmrA,n-2(x),n≥2,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} r_{A,n}(x)=f_{n}(x)r_{A,n-1}(x)-v_{n}x^{m}r_{A,n-2}(x),\\;n\\ge 2, \\end{aligned}$$\\end{document}where the initial polynomials r_{A,0}, r_{A,1}in K[x] are of degree i, j respectively and f_{n}in K[x], nge 2, is of degree k with variable coefficients. The aim of the paper is to prove the formula for the resultant {text {Res}}(r_{A,n}(x),r_{A,n-1}(x)). Our result is an extension of the classical Schur formula which is obtained for A=(0,1,1,0). As an application we get the formula for the resultant {text {Res}}(r_{A,n},r_{A,n-2}), where the sequence (r_{A,n})_{nin mathbb {N}} is the sequence of orthogonal polynomials corresponding to a moment functional which is symmetric.