The nth Catalan number also counts the number of ways that we can break up a regular polygon with n+2 sides into triangles by means of diagonals that do not cross one another, and there are other interpretations along these lines. As with binomial coefficients, there are formulas relating Catalan numbers to smaller Catalan numbers, which makes them amenable to manipulation.
Fibonacci numbers
The Fibonacci sequence is one series of numbers that engenders wide fascination among the general public. The sequence runs as follows