Multifactorial

A generalization of the Factorial and Double Factorial,

$$n! = n(n-1)(n-2)\cdots 2\cdot 1$$

$$n!! = n(n-2)(n-4)\cdots$$

$$n!!! = n(n-3)(n-6)\cdots,$$

etc., where the product runs through positive integers. The Factorials $n!$ for $n=1$, 2, ..., are 1, 2, 6, 24, 120, 720, ... (Sloane's A000142); the Double Factorials $n!!$ are 1, 2, 3, 8, 15, 48, 105, ... (Sloane's A006882); the triple factorials $n!!!$ are 1, 2, 3, 4, 10, 18, 28, 80, 162, 280, ... (Sloane's A007661); and the quadruple factorials $n!!!!$ are 1, 2, 3, 4, 5, 12, 21, 32, 45, 120, ... (Sloane's A007662).

See also Factorial, Gamma Function

References

Sloane, N. J. A. Sequences A000142/M1675, A006882/M0876, A007661/M0596, and A007661/M0534 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.