An antichain of a poset $(P, <)$ is a subset of pairwise incomparable elements, namely, a subset $A \subseteq P$ such that there are no $x, y \in A$ with $x < y$. By a result of Provan and Ball, it is known that it is #P-hard, given a poset, to compute its number of antichains.
My question is whether this hardness result is known to extend to restricted classes of posets. More specifically, I am interested in posets which are distributive lattices. Is it #P-hard to count antichains in distributive lattices?
Of course, one could also ask for which classes of posets is hardness, or tractability, known to hold. Has there been any work on this since Provan and Ball?