  An alternative and combinatorial proof is given for a connection between a
system of Hahn polynomials and identities for symmetric elements in the
Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys.
Rev. Lett. 56 (1986), J. Math. Phys. 28, 509 (1987)] and proved by Koornwinder
[J. Phys. Phys. 30(4), 1989]. In the same vein two results announced by Bender
and Dunne [J. Math. Phys. 29 (8), 1988] connecting a special one-parameter
class of Hermitian operator orderings and the continuous Hahn polynomials are
also proved.
