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Adding the decimal expansion for 100! is somehow triggering the spam filter. I've reported the issue, and I hope this gets fixed soon. For now, the number is broken in two. FB100Ztalkcontribs 18:31, September 6, 2012 (UTC)

Original variation[]

Jiawhein wrote in his sandbox about "half factorial", which he defined as \(0.5 \times 1 \times 1.5 \times 2 \cdots (n-1) \times (n-0.5) \times (n)\). I will correct and generalize that definition: let \(!(n,m) = 1 \times {1 \over m} \times {2 \over m} \times {3 \over m} \cdots 2 \times (2+{1 \over m}) \times (2+{2 \over m}) \cdots \cdots n\).

For example:

\(!(2,2) = 1 \times 1.5 \times 2\)

\(!(2,3) = 1 \times (1+{1 \over 3}) \times (1+{2 \over 3}) \times 2\)

\(!(2,4) = 1 \times 1.25 \times 1.5 \times 1.75 \times 2\)

\(!(3,2) = 1 \times 1.5 \times 2 \times 2.5 \times 3\).

It really makes some novelty to the factorial extensions.

Ikosarakt1 (talk ^ contribs) 19:07, April 10, 2013 (UTC)

Yes, but \(0.5 \times 1 \times 1.5 \times 2 \cdots (n-1) \times (n-0.5) \times (n)={1 \over 2}\times{2 \over 2}\times{3 \over 2}\cdots {2n-1 \over 2}\times{2n \over 2}={(2n)! \over 2^{2n}}\). Similarily, \(!(n,m)={(mn)! \over m^{mn}}\). So this isn't big generalization. LittlePeng9 (talk) 19:14, April 10, 2013 (UTC)

Actually, I don't include 0.5 in expression at the term, because it divides the result by 2, so it doesn't make advantage. I decided to start with 1. Ikosarakt1 (talk ^ contribs) 19:19, April 10, 2013 (UTC)

If so, result \(!(n,m)={(mn)! \over m!\times m^{m(n-1)}}\). LittlePeng9 (talk) 19:32, April 10, 2013 (UTC)

Half factorial is based on double factorial while the fraction factorial is based on the multifactorial. \(a\)\(l\)\(t\) 09:40, May 18, 2013 (UTC)

No second entry; is amount of !'s. \(a\)\(l\)\(t\) 10:29, May 26, 2013 (UTC)

Intorial (oppsite of factorial)[]

Define n-!=f(n) as the Intorial of n (n must be a value of factorial):

define a number z=1.

now do the next steps:

1.if n equal to 1,stop the steps and exit

2.z=z+1

3.n=n\z

4.repeat the steps

for example:

\(120/2/3/4/5\) =1 => \(120-!=5\) 

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