: Mathématiques: double factorial

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double factorial

In mathematics, the double factorial of a number $n$ , denoted by $n ‼$ , is the product of all the positive integers up to $n$ that have the same parity (odd or even) as $n$ . That is, ${\\displaystyle n!!=\\prod _{k=0}^{\\left\\lceil {\ rac {n}{2}}\ ight\ ceil -1}(n-2k)=n(n-2)(n-4)\\cdots .}$ Restated, this says that for even $n$ , the double factorial is ${\\displaystyle n!!=\\prod _{k=1}^{\ rac {n}{2}}(2k)=n(n-2)(n-4)\\cdots 4\\cdot 2\\,,}$ while for odd $n$ it is ${\\displaystyle n!!=\\prod _{k=1}^{\ rac {n+1}{2}}(2k-1)=n(n-2)(n-4)\\cdots 3\\cdot 1\\,.}$ For example, $9‼ = 9 \times 7 \times 5 \times 3 \times 1 = 945$ . The zero double factorial $0‼ = 1$ as an empty product
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Double_factorial)

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