  We give a formula for the bivariate generating function of a stationary
1-dependent counting process in terms of its run probability generating
function, with a probabilistic proof. The formula reduces to the well known
bivariate generating function of the Eulerian distribution in the case of
descents of a sequence of indepependent and identically distributed random
variables. The formula is compared with alternative expressions from the theory
of determinantal point processes and the combinatorics of sequences.
