Home Algorithms Recursion Find Nth Catalan Number
C
0
=
C
1
=
1
and
C
n
=
( 2 n ) ! ( ( n + 1 ) ! n ! )
=
∑
i = 0 n - 1
C
i
C
n - 1 - i
=
2 ( 2 n - 1 ) n + 1
C
n - 1
for
n
>
2
Hint
Observe recursive relationship from definition, C(n) is sum of C(i) times C(n - 1 - i) from i = 0 to i < n, create recurisive function calls. The second form of recursive relationship is drived by C(n) / C(n - 1), simplify its equation, then move C(n - 1) to the right.
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