FACTDOUBLE function

FACTDOUBLE(n) returns the double factorial of n.

The double factorial of a number n, denoted by n!!, is the product of all the positive integers up to n that have the same parity (odd or even) as n.

If n is even, the double factorial is

$$ n!! = \prod_{k=1}^\frac{n}{2} (2k) = n(n-2)(n-4)\cdots 4\cdot 2 $$

If n is odd, the double factorial is

$$ n!! = \prod_{k=1}^\frac{n+1}{2} (2k-1) = n(n-2)(n-4)\cdots 3\cdot 1 $$

For example, $ 9‼ {{=}} 9 × 7 × 5 × 3 × 1 {{=}} 945 $.

If the argument n is not an integer, it is truncated.
The argument n cannot be negative.
If the even number n is larger than 300, or if the odd number n is larger than 263, the function overflows and returns an error.
The argument n can be a real number or a matrix. When it is a matrix, the function returns a matrix with the same dimensions and with the FACTDOUBLE function applied to all elements.

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