Catalan numbers form a sequence of natural numbers that occur in various counting problems.

**Series is**

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452…. and so on.

**Application**

This sequence is very popular in many combinatorial problems. More on application of Catalan Numbers here

**Formula**

The *n*^{th} Catalan number is given directly in terms of binomial coefficients by

**C _{n} = ^{2n}C_{n}/(n+1) = 2n!/{(n+1)!n!}**

we can also use this formula

C_{0} = 1

C_{n} = C_{n-1}*(4n-2)/(n+1)

cat=[] #1st term is 1 cat.append(1) for i in range (1,1001): x=cat[i-1]*(4*i-2)/(i+1) cat.append(x) def CatalanNumber(n): return cat[n]Advertisements