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#1 2022-05-12 21:50:47

ganesh
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Registered: 2005-06-28
Posts: 38,059

Double Factorial

In mathematics, the double factorial or semifactorial of a number n, denoted by n‼, is the product of all the integers from 1 up to n that have the same parity (odd or even) as n. That is,

For even n, the double factorial is

and for odd n it is

For example, 9‼ = 9 × 7 × 5 × 3 × 1 = 945. The zero double factorial 0‼ = 1 as an empty product.

The sequence of double factorials for even n = 0, 2, 4, 6, 8,... starts as

1, 2, 8, 48, 384, 3840, 46080, 645120,...

The sequence of double factorials for odd n = 1, 3, 5, 7, 9,... starts as

1, 3, 15, 105, 945, 10395, 135135,...

The term odd factorial is sometimes used for the double factorial of an odd number.


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