Let $A$ be a set has $n$ element, my question is how many partial order on it?
For $n=0,1$, $N_P(n)=1$ Case $n=2$, $N_P(n)=3$ Case $n=3$, $N_P(n)=19$
Is there a general formula?
It seems closed formula have not been found yet. But does any generating function be known current?