  Almkvist and Meurman showed that if h and k are integers, then so is
$k^n(B_n(h/k) - B_n)$ where $B_n(u)$ is the Bernoulli polynomial. We give here
a new and simpler proof of the Almkvist-Meurman theorem using generating
functions. We describe some properties of these numbers and prove a common
generalization of the Almkvist-Meurman theorem and a result of Gy on
Bernoulli-Stirling numbers. We then give a simple generating function proof of
an analogue of the Almkvist-Meurman theorem for Euler polynomials, due to Fox.
