A multifactorial is a generalization of the factorial
and double factorial,
etc., where the products run through positive integers.
For a nonnegative integer 
and a positive integer 
, write 
for the multifactorial with step 
. A finite product and a Pochhammer
symbol representation are
 |
(4)
|
where ![m=[n/k]](/images/equations/Multifactorial/Inline14.svg)
and ![[x]](/images/equations/Multifactorial/Inline15.svg)
is the ceiling function. The empty
product gives 
.
The following table lists the values of the first few multifactorials for 
, 2, ....
 | A000142 | 1, 2, 6, 24, 120, 720, ... |
 | A006882 | 1, 2, 3, 8, 15, 48, 105, ... |
 | A007661 | 1, 2, 3, 4, 10, 18, 28, 80, 162, 280, ... |
 | A007662 | 1,
2, 3, 4, 5, 12, 21, 32, 45, 120, ... |
See also
Double Factorial,
Factorial,
Gamma Function,
Pochhammer
Symbol,
Reciprocal Multifactorial
Constant
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References
Sloane, N. J. A. Sequences A000142/M1675, A006882/M0876, A007661/M0596,
and A007662/M0534 in "The On-Line Encyclopedia
of Integer Sequences."Referenced on Wolfram|Alpha
Multifactorial
Cite this as:
Weisstein, Eric W. "Multifactorial." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Multifactorial.html
Subject classifications
