  Let $I_{n,m} = (x_1\cdots x_{m},x_2 \cdots
x_{m+1},\ldots,x_{n+1}x_{n+2}\cdots x_{n+m})$ be the $m$-path ideal of a path
of length $n + m-1$ over a polynomial ring $S =
\mathrm{k}[x_1,\ldots,x_{n+m}]$. We compute all the graded Betti numbers of all
powers of $I_{n,m}$.
