   number of binary trees ..
  Hi , How to calculate how many binary trees can be made with n nodes ..regardsy2jsave   
  By binary tree's I assume you mean branches, in which case there is a branch per node so there will be n branches.You need to be a bit more clear on what you mean.   ;  If it's left-balanced: exactly one ;-)   ;  There are several ways of counting them. Perhaps if you tell us how many trees you think there are for n=1, n=2 and n=3, we can deduce exactly what you mean. The answer will most likely involve Catalan numbers.   ;  Eric Lippert just did a series on binary trees and other things, search for his msdn blog, that will probably answer your question.   ;  I see several possible interpretations of this badly written question. Here are some of them:1. What is the most number of binary trees I can construct at once using N nodes?2. How many ways can a single binary tree containing N nodes be structured?3. How many distinct but ordered binary trees could I produce given N different nodes to play with where not all must be used at once?4. How many distinct binary trees could I produce given N different nodes to play with where not all must be used at once?Examlpes of each with 3 nodes:1: X X X    Answer = 3 [razz]2:  XX   X    XX   /    /    / \\    \   X   XX   X X   X    Answer = 5 /\    /\ X  X  X  X3: A B CandA   A   BB   C   C \   \   \   /   /   /  B   C   C A   A   BandAA  \    \C   B   ... etc   Answer = 14   /\   B  C4: A B CandA   A   B   B   C   CA   A   B   B   C   C \   \   \   \   \   \   /   /   /   /   /   /  B   C   A   C   A   B B   C   A   C   A   BandAB  \\BA ... etc   Answer = 45 (I think)   //  CC