Consider the formula above. Have you notice that there are expressions F(0)*F(n-1) and F(n-1)*F(0) ? If you set F(0) as 0 then F(n-1) will be cancelled out. We need to keep the F(n-1), so , We have to set F(0) as 1.
bbe like that
calculate the Cantalan numer or why is Cantalan number?
It is a math theory, you can find the similar proof stack pop sequence.
A equivalent problem the stack pop sequence.for exam, 1 2 3 4,the stack pop sequence may be 3 4 2 1, but 4 2 3 1 is wrong. each pop sequence is compared to mid-order transverse , while the origin sequence like 1 2 3 4 compared to pre-order transverse. And as you see, we can build the unique BST with the pre-order and mid-order.