Let $\Pi$ be a parametrized counting problem, where the parameter is the solution cost, e.g. counting the number of $k$-sized vertex cover in a graph, parametrized by $k$.
Assume that $\Pi$ is $\#W$-complete (a known problem for example would be counting the number of simple paths of length $k$ in a graph).
Note that when discussing a parameter which is the cost of solution it makes sense to discuss the approximation hardness (e.g. see this question), as opposed to other popular parametrizations.