  Recently a definition for a Lorentz invariant operator approximating the
d'Alembertian in d-dimensional causal set space-times has been proposed. This
operator contains several dimension-dependent constants which have been
determined for d=2,...,7. In this note we derive closed form expressions for
these constants, which are valid in all dimensions. Using these we prove that
the causal set action in any dimension can be defined through this discrete
d'Alembertian, with a dimension independent prefactor.
