Adding the double factorial algorithm (#4550)

maths/double_factorial_recursive.py

@@ -0,0 +1,31 @@
+def double_factorial(n: int) -> int:
+    """
+    Compute double factorial using recursive method.
+    Recursion can be costly for large numbers.
+
+    To learn about the theory behind this algorithm:
+    https://en.wikipedia.org/wiki/Double_factorial
+
+    >>> import math
+    >>> all(double_factorial(i) == math.prod(range(i, 0, -2)) for i in range(20))
+    True
+    >>> double_factorial(0.1)
+    Traceback (most recent call last):
+        ...
+    ValueError: double_factorial() only accepts integral values
+    >>> double_factorial(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: double_factorial() not defined for negative values
+    """
+    if not isinstance(n, int):
+        raise ValueError("double_factorial() only accepts integral values")
+    if n < 0:
+        raise ValueError("double_factorial() not defined for negative values")
+    return 1 if n <= 1 else n * double_factorial(n - 2)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()