No. of possible ordered binary trees with n nodes ? I know that for n=3 answer is 12. Is there any direct for for calculating it?

how can you say that answer for n=3 is 12…as i think that it would be 5 because it can be related that a binary tree can be related by parenthesis then for n=3 we have 5 parenthesizing ways which are ((())) ()(()) ()()() (())() (()()).

by my view

you can read about it on [http://en.wikipedia.org/wiki/Catalan_number][2].it best describes use and application of Catalan number in various combinatorial problems

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