  For the computation of terms of the Baker-Campbell-Hausdorff series $H =
\log(e^Ae^B})$ some a priori knowledge about the denominators of the
coefficients of the series can be beneficial. In this paper an explicit formula
for the computation of common denominators for the rational coefficients of the
homogeneous components of the series is derived. Explicit computations up to
degree 30 show that the common denominators obtained by this formula are as
small as possible, which suggests that the formula is in a sense optimal. The
sequence of integers defined by the formula seems to be interesting also from a
number-theoretic point of view. There is, e.g., a connection with the
denominators of the Bernoulli numbers and the Bernoulli polynomials.
