My exact divide-conquer algorithm for counting antichain in a poset?
Counting antichains in an $n$ element poset is equivalent to counting independent sets in a comparability graph on $n$ vertices. The problem of counting the independent sets in an $n$ vertex graph has an $O(1.2461^n)$ time algorithm, see Fürer and Kasiviswanathan http://eccc.hpi-web.de/report/2005/033/ .