On the expansion of C[varrho]*(V + I) as a sum of zonal polynomials

The coefficients a[tau][varrho], sometimes called "generalized binomial coefficients" in the expansion C[varrho]*(V +I) = [Sigma][tau]a[varrho][tau]C[tau]*(V), are computed explicitly when t = r + 1, where [varrho] is a partition of r and [tau] a partition of t. A recursion formula permits the calculation of the general a[tau][varrho]. Several properties of a[tau][varrho] are proved. A connection between the a[tau][varrho] and other coefficients is established. The main tools used are Bingham's identity, results from the theory of invariant differential operators, and a lemma concerning zonal polynomials.