  The equivariant Hilbert series of an ideal generated by an orbit of a
monomial under the action of the monoid $\mbox{Inc}(\mathbb{N})$ of strictly
increasing functions is determined. This is used to find the dimension and
degree of such an ideal. The result also suggests that the description of the
denominator of an equivariant Hilbert series of an arbitrary
$\mbox{Inc}(\mathbb{N})$-invariant ideal as given by Nagel and R\"omer is
rather efficient.
