  The series expansion of a power of the modified Bessel function of the first
kind is studied. This expansion involves a family of polynomials introduced by
C. Bender et al. New results on these polynomials established here include
recurrences in terms of Bell polynomials evaluated at values of the Bessel zeta
function. A probabilistic version of an identity of Euler yields additional
recurrences. Connections to the umbral formalism on Bessel functions introduced
by Cholewinski are established.
