Integer sequences | Factorial and binomial topics | Enumerative combinatorics
Double factorial
In mathematics, the double factorial or semifactorial of a number n, denoted by n‼, is the product of all the integers from 1 up to n that have the same parity (odd or even) as n. That is, For even n, the double factorial is and for odd n it is For example, 9‼ = 9 × 7 × 5 × 3 × 1 = 945. The zero double factorial 0‼ = 1 as an empty product. The sequence of double factorials for even n = 0, 2, 4, 6, 8,... starts as 1, 2, 8, 48, 384, 3840, 46080, 645120,... (sequence in the OEIS) The sequence of double factorials for odd n = 1, 3, 5, 7, 9,... starts as 1, 3, 15, 105, 945, 10395, 135135,... (sequence in the OEIS) The term odd factorial is sometimes used for the double factorial of an odd number. (Wikipedia).
