Add Catalan number to maths (#6845)

* Add Catalan number to maths

* updating DIRECTORY.md

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Author: 3 people

Diff for: DIRECTORY.md

@@ -475,6 +475,7 @@
   * [Binomial Coefficient](maths/binomial_coefficient.py)
   * [Binomial Distribution](maths/binomial_distribution.py)
   * [Bisection](maths/bisection.py)
+  * [Catalan Number](maths/catalan_number.py)
   * [Ceil](maths/ceil.py)
   * [Check Polygon](maths/check_polygon.py)
   * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
@@ -632,8 +633,9 @@
 
 ## Physics
   * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py)
-  * [Lorenz Transformation Four Vector](physics/lorenz_transformation_four_vector.py)
+  * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py)
   * [N Body Simulation](physics/n_body_simulation.py)
+  * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py)
   * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py)
 
 ## Project Euler

Diff for: maths/catalan_number.py

@@ -0,0 +1,51 @@
+"""
+
+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):
+        raise TypeError(f"Input value of [number={number}] must be an integer")
+
+    if number < 1:
+        raise ValueError(f"Input value of [number={number}] must be > 0")
+
+    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()