Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

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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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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imcute

Member

Registered: 2022-09-28

Posts: 176

Re: Double Factorial

i made a continuation for this thing https://www.mathisfunforum.com/viewtopic.php?pid=429787#p429787 (yes u linked to it yesterday) did i do it correct?