$R_I$ biorthogonal polynomials of Hahn type

A finite family of $R_I$ polynomials is introduced and studied. It consists in a set of polynomials of ${}_3{F}_2$ form whose biorthogonality to an ensemble of rational functions is spelled out. These polynomials are shown to satisfy two generalized eigenvalue problems: in addition to their recurrence relation of $R_I$ type, they are also found to obey a difference equation. Underscoring this bispectrality is a triplet of operators with tridiagonal actions.