Powers of staircase Schur functions and symmetric analogues of Bessel polynomials

We present several identities involving staircase Schur functions. These identities are then interpreted in terms of a sequence of orthogonal polynomials in one variable x, with coefficients in the ring of symmetric functions. By an appropriate specialization these polynomials reduce to Bessel polynomials. This leads to a new determinantal expression for Bessel polynomials and suggests that their combinatorics might be linked to Young tableaux or shifted Young tableaux.