`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.