I saw this sequence on the Online Encyclopedia of Integer Sequences, which describe the number of 3-element proper antichains of an n-element set.
What does it mean to be a 3-element proper antichain of an n-element set? Suppose the set is $\{1,2,\ldots,n\}$. A $3$-element antichain could be something like $\{1,2\},\{1,3\},\{2,4\}$, where any two sets are incomparable. Now what does "proper" mean?