A lattice path is a path from the origin to the destination where each step is either up or right. Clearly, the number of all the paths from `(0,0)` to `(n,n)` is equal to `((2n),(n))`.
`a(n)` is the number of lattice paths from `(0,0)` to `(n,n)` without hitting `(0,1)` or `(n,n-1)`. For example, a path from `(0,0)` to `(5,5)` hitting `(0,1)` but not hitting `(5,4)` is drawn in the following figure.
Find `a(n)`.
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Updated 03/15/2015
Typos are fixed.