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.
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.
