# Python Math: nth Catalan Number

## Python Math: Exercise-25 with Solution

Write a Python program for the nth Catalan numbers.

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène Charles Catalan (1814–1894).

Using zero-based numbering, the nth Catalan number is given directly in terms of binomial coefficients by

The first Catalan numbers for n = 0, 1, 2, 3, … are

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, ....

**Pictorial Presentation**

The C5 = 42 noncrossing partitions of a 5-element set (below, the other 10 of the 52 partitions)

Image Credits: Watchduck

**Sample Solution**:

**Python Code:**

```
def catalan_number(num):
if num <=1:
return 1
res_num = 0
for i in range(num):
res_num += catalan_number(i) * catalan_number(num-i-1)
return res_num
for n in range(10):
print(catalan_number(n))
```

Sample Output:

1 1 2 5 14 42 132 429 1430 4862

**Flowchart:**

**Python Code Editor:**

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