  We study the Euler-Frobenius numbers, a generalization of the Eulerian
numbers, and the probability distribution obtained by normalizing them. This
distribution can be obtained by rounding a sum of independent uniform random
variables; this is more or less implicit in various results and we try to
explain this and various connections to other areas of mathematics, such as
spline theory.
  The mean, variance and (some) higher cumulants of the distribution are
calculated. Asymptotic results are given. We include a couple of applications
to rounding errors and election methods.
