Reinventing Catalan numbers
Counting binary trees I was thinking about of the problem of balancing a binary tree, and my mind stumbled across to the question “How many different binary trees with labelled nodes can you make without changing the traversal order?”. After figuring out the answer myself I realized that the numbers of such binary trees are just Catalan numebrs (I was not really into combinatorics - now I am). For example, the following has traversal order 1->2->3->4->5->6->7...