  This note is devoted to study the recurrent numerical sequence defined by:
$a_0 = 0$, $a_n = \frac{n}{2} a_{n - 1} + (n - 1)!$ ($\forall n \geq 1$).
Although, it is immediate that ${(a_n)}_n$ is constituted of rational numbers
with denominators powers of $2$, it is not trivial that ${(a_n)}_n$ is actually
an integer sequence. In this note, we prove this fact by expressing $a_n$ in
terms of the Genocchi numbers and the Stirling numbers of the first kind. We
derive from our main result several corollaries and we conclude with some
remarks and open problems.
