  In this paper, a single sum formula for the linearization coefficients of the
Bessel polynomials is given. In three special cases this formula reduces indeed
to either Atia and Zeng's formula (Ramanujan Journal, Doi
10.1007/s11139-011-9348-4) or Berg and Vignat's formulas in their proof of the
positivity results about these coefficients (Constructive Approximation, {\bf
27} (2008), 15-32). As a bonus, a formula reducing a sum of hypergeometric
functions $_3F_2$ to $_2F_1$ is obtained.
