  The factorial moments of the standard Poisson distribution are well known and
are simple, but the raw moments are considered to be more complicated (Touchard
polynomials). The present note presents a recurrence relation and an explicit
combinatorial sum for the raw moments of the Poisson distribution of order $k$.
Unlike the standard Poisson distribution (the case $k=1$), for $k>1$ the
structure of the raw and factorial moments have many similarities and the raw
moments are not more complicated (formally, at least) than the factorial
moments. We remark briefly on the central moments (i.e.~moments centered on the
mean) of the Poisson distribution of order $k$.
