PlanetMath: double factorial

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double factorial

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The double factorial of a positive integer is the product of the positive integers less than or equal to that have the same parity as , that is,

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

where

denotes

is an odd number and

For example,

$\displaystyle 7!! = 7 \cdot 5 \cdot 3 \cdot 1 = 105$

$\displaystyle 10!! = 10\cdot 8\cdot 6\cdot 4\cdot 2 = 3840$

Note that is not the same as .

Observe that and $(2n+1)!! = \frac{(2n+1)!}{2^n n!}$ .

"double factorial" is owned by drini. [ full author list (5) | owner history (5) ]

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Cross-references: even number, odd number, parity, product, integer, positive
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This is version 6 of double factorial, born on 2002-02-20, modified 2005-07-26.
Object id is 2318, canonical name is DoubleFactorial.
Accessed 4187 times total.

Classification:

05A10 (Combinatorics :: Enumerative combinatorics :: Factorials, binomial coefficients, combinatorial functions)

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