It is well-known that the number of linear extensions of the following Hasse diagram is counted by Catalan number `C_n=\frac{1}{n+1}((2n),(n))`.
Now we consider the number of linear extensions of following diagrams `D_n`. `D_1`, `D_2` and `D_3` are drawn as follows. One can easily figure out what `D_n` looks like.
`a(n)` is the number of linear extensions of `D_n`.
Find `a(n)`.