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Multifactorial


A generalization of the factorial and double factorial,

n!=n(n-1)(n-2)...2·1
(1)
n!!=n(n-2)(n-4)...
(2)
n!!!=n(n-3)(n-6)...,
(3)

etc., where the products run through positive integers.

The following table lists the values of the first few multifactorials for n=1, 2, ....

n!A0001421, 2, 6, 24, 120, 720, ...
n!!A0068821, 2, 3, 8, 15, 48, 105, ...
n!!!A0076611, 2, 3, 4, 10, 18, 28, 80, 162, 280, ...
n!!!!A0076621, 2, 3, 4, 5, 12, 21, 32, 45, 120, ...

See also

Double Factorial, Factorial, Gamma Function, Pochhammer Symbol, Reciprocal Multifactorial Constant

Explore with Wolfram|Alpha

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 Web Resource. https://mathworld.wolfram.com/Multifactorial.html

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