Double Factorial

The double factorial of a positive integer n, written n followed by two exclamation points, is the product of all the positive integers up to n that share the same parity as n, so that for even n it is the product of every even number from n down to 2, and for odd n it is the product of every odd number from n down to 1; for instance 5 double factorial equals 5 times 3 times 1, or 15, and 6 double factorial equals 6 times 4 times 2, or 48. Both 0 double factorial and negative-one double factorial are conventionally treated as empty products equal to 1, the term odd factorial is sometimes used specifically for the double factorial of an odd number, and a separate definition extends the double factorial to most complex numbers as well.