You need to know a equation to solve this problem ( Catalen number).

A non empty binary tree consists of a root X, a left sub-tree L, and a right sub-tree R. Let n be the size of the binary tree, let nL= | L | the size of L, nR = | R | = the size of R. Then n = 1 + nL + nR. So there are only n different possible of pair (nL,nR). Suppose if n=6, the only possibility are (0,5),(1,4),(2,3),(3,2),(4,1) or (5,0). So in the closed form the formula is,

f(n) =

First you find all the tree type for all nodes 1 to 25 ( I am talking about pre-calculation), because 25 is enough for the given input. 

Remember for 14 the output is 4 and for 13 the output is also 4.