Catalan Number

P
D
A
p
```"""

Calculate the nth Catalan number

Source:
https://en.wikipedia.org/wiki/Catalan_number

"""

def catalan(number: int) -> int:
"""
:param number: nth catalan number to calculate
:return: the nth catalan number
Note: A catalan number is only defined for positive integers

>>> catalan(5)
14
>>> catalan(0)
Traceback (most recent call last):
...
ValueError: Input value of [number=0] must be > 0
>>> catalan(-1)
Traceback (most recent call last):
...
ValueError: Input value of [number=-1] must be > 0
>>> catalan(5.0)
Traceback (most recent call last):
...
TypeError: Input value of [number=5.0] must be an integer
"""

if not isinstance(number, int):
msg = f"Input value of [number={number}] must be an integer"
raise TypeError(msg)

if number < 1:
msg = f"Input value of [number={number}] must be > 0"
raise ValueError(msg)

current_number = 1

for i in range(1, number):
current_number *= 4 * i - 2
current_number //= i + 1

return current_number

if __name__ == "__main__":
import doctest

doctest.testmod()
```