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I think total number of binary trees possible for n nodes is equal to Catalan number
C(n) = (2n)! / ((n+1)! * n!)
for n = 4, 14 binary trees are possible as given by catalan number. While 2^n-n = 12. for n=4

Hi Amit,
For a binary “search” tree, the possible combinations is C(n), the Catalan number, we are talking about binary trees in general.
Thanks for the extra information though. :)

## 4 comments

(2n)!/(n+1)! is the answer.

Catalan Number is for BST

no you are wrong the number of possible binary trees with 4 nodes is 14, but 2^4-4 is not 14.

I think total number of binary trees possible for n nodes is equal to Catalan number

C(n) = (2n)! / ((n+1)! * n!)

for n = 4, 14 binary trees are possible as given by catalan number. While 2^n-n = 12. for n=4

http://en.wikipedia.org/wiki/Catalan_number

Hi Amit,

For a binary “search” tree, the possible combinations is C(n), the Catalan number, we are talking about binary trees in general.

Thanks for the extra information though. :)