Constant distribution in the factorial 2n!

Question

a very simple question: how does 2 distribute in the factorial $2n!$ ?

$2((n)(n-1)(n-2))$

would be treating the expression as $2(n!)$, which is different from:

$(2n)(2n-1)(2n-2)$

which is different still from:

$(2(n))(2(n-1))(2(n-2))$

Thanks.

Answer 1

Your first expression is $2(n!)$, your second is $(2n)!$ and the third is $(2n)!!$ The fist two possibilities give a good reason to use parentheses-they are quite different. I think $(2n)!$ would be the default reading if there are no parentheses, but I would look for confirmation in whatever I was reading.