Decomposing a Factorial into Large Factors

Re:Decomposing a Factorial into Large Factors by phkahler on Friday March 28, 2025 @03:39PM (#43509202)

Is there a standard notation for the product of all even numbers up to N and for the product of all odd numbers up to N? I know if N is even then the product of evens is = (N/2)! * 2^(N/2) so I guess notation for that is a little redundant, but there is no simple formula for the product of the odd numbers.

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Re:Decomposing a Factorial into Large Factors by madcaptenor on Friday March 28, 2025 @03:45PM (#43509238)

N!! is the usual notation, so 3!! = 3, 4!! = 8, 5!! = 15, 6!! = 48, etc.

It’s a bit unfortunate, because you’d think it meant iterating the factorial, so 3!! = 720, etc. But there are basically no situations where you want to do that.

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Re:Decomposing a Factorial into Large Factors by thrasibule on Friday March 28, 2025 @03:45PM (#43509240)

N!! is pretty standard I think.

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Re:Decomposing a Factorial into Large Factors by Someone on Friday March 28, 2025 @04:20PM (#43509488)

> but there is no simple formula for the product of the odd numbers.

There is. It is N! divided by the product of all even numbers up to N.

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