$a(n)$ is the number of linear extensions of poset $P_n$.
One can figure out what the Hasse diagram of $P_n$ is by observing Hasse diagrams of $P_1$, $P_2$, $P_3$, $P_4$ and $P_5$ in the picture.
Find $a(n)$.
$a(n)$ is the number of linear extensions of poset $P_n$.
One can figure out what the Hasse diagram of $P_n$ is by observing Hasse diagrams of $P_1$, $P_2$, $P_3$, $P_4$ and $P_5$ in the picture.
Find $a(n)$.
Updated 06/11/2015 and remarked by Ran Pan
We obtained a recursive formual for $a(n)$ and for $n\ge 1$, the the first several terms are $1, 6, 71, 1266, 30206, 902796, 32420011, \cdots$. A solution will be posted here soon but an explicit formula of $a(n)$ is not found yet.Updated 06/28/2016 and remarked by Ran Pan
Sorry for such a loooong delay! An algorithmic solution is posted here.