  In this short paper, the commutator of monomials of operators obeying
constant commutation relations is expressed in terms of anticommutators. The
formula involves Bernoulli numbers or Euler polynomials evaluated in zero. The
role of Bernoulli numbers in quantum-mechanical identities such as the
Baker-Campbell-Hausdorff formula is emphasized and applications connected to
ordering problems as well as to Ehrenfest theorem are proposed.
