Factorials and anti-factorials Supposing n¡ (the inverted spanish exclamation mark - as opposed to n!) uses sequential divisions, is it always true that n ! ∗ n ¡ = n 2 ? Example: For n = 7, n ¡ = 7 ÷ 6 ÷ 5 ÷ 4 ÷ 3 ÷ 2 = 0.00972222222222222222222222222222. If you multiply this number by 5040 (=7!) you get 49.I've read the directions in the help center and could not understand why it is off topic. It is like asking about the relation between x ∗ x = x 2 and x ÷ x ÷ x ÷ x = x − 2 . In fact, I could not determine if this kind of question is on-topic either. And I think there is not a sister-site that would accept such kind of questions (I checked all of them). Anyways, my question has been answered. I was lazy when I failed to do some calculations to find the answer myself. This was my very first time here. I've learned something. Thank you.

Question

Factorials and anti-factorials Supposing n¡ (the inverted spanish exclamation mark - as opposed to n!) uses sequential divisions, is it always true that   n  !  ∗  n      ¡    =      n    2  ? Example: For n = 7,   n      ¡    =  7  ÷  6  ÷  5  ÷  4  ÷  3  ÷  2  =  0.00972222222222222222222222222222. If you multiply this number by 5040 (=7!) you get 49.I&#039;ve read the directions in the help center and could not understand why it is off topic. It is like asking about the relation between   x  ∗  x  =      x    2   and   x  ÷  x  ÷  x  ÷  x  =      x          −      2      . In fact, I could not determine if this kind of question is on-topic either. And I think there is not a sister-site that would accept such kind of questions (I checked all of them). Anyways, my question has been answered. I was lazy when I failed to do some calculations to find the answer myself. This was my very first time here. I&#039;ve learned something. Thank you.

empatiji2v · Accepted Answer

By your definition it&#039;s      n          (      n      −      1      )      !        ⋅  n  !  =      n    2

Leroy Gray · Accepted Answer

Your definition amounts to  n      ¡    =      n          (      n      −      1      )      !      so for instance, we would compute   7      ¡    =  7      /    (  6  !  ). Clearly, then, we have  (  n  !  )  ⋅  (  n      ¡    )  =  [  n  ⋅  (  n  −  1  )  !  ]  ⋅      n          (      n      −      1      )      !        =      n    2

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