Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

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.


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.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

#2 2022-12-25 22:50:58

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?

Offline

Board footer

Powered by FluxBB