  We show how Viennot's combinatorial theory of orthogonal polynomials may be
used to generalize some recent results of Sukumar and Hodges on the matrix
entries in powers of certain operators in a representation of su(1,1). Our
results link these calculations to finding the moments and inverse polynomial
coefficients of certain Laguerre polynomials and Meixner polynomials of the
second kind. As an immediate consequence of results by Koelink, Groenevelt and
Van Der Jeugt, for the related operators, substitutions into essentially the
same Laguerre polynomials and Meixner polynomials of the second kind may be
used to express their eigenvectors. Our combinatorial approach explains and
generalizes this "coincidence".
