Problem 6: Double Factorial (100pts)

Let's write a function double_factorial, which takes a positive integer \( n \) and returns its double factorial.

Double factorial of a positive integer \( n \), denoted by \( n!! \), is defined as

\[ n!! = \prod_{i=0}^{\lceil \frac{n}{2} \rceil - 1} (n - 2i) = n \times (n - 2) \times (n - 4) \times \dots \]

This problem is an advanced version of Problem 2, Lab 01.

def double_factorial(n, k):
    """Compute the double factorial of n.

    >>> double_factorial(6)  # 6 * 4 * 2
    48
    >>> double_factorial(5)  # 5 * 3 * 1
    15
    >>> double_factorial(3)  # 3 * 1
    3
    >>> double_factorial(1)  # 1
    1
    """
    "*** YOUR CODE HERE ***"