1. The problem statement, all variables and given/known data There are 2n points on a circle, we want to connect each two of them to make a pattern of connection in the way that there is no cross between the lines of connection, and all the lines have to be inside the circle and on the plane of the circle. Question: How many different patterns of connection there are? 2. Relevant equations This is a relevant question to count the number of planar Feynman Diagrams that without interaction insider a loop. 3. The attempt at a solution we can check that in the case of n=1, there is 1 pattern, n=2, there are 2 different patterns, n=3, there are 5 different patterns.