Double factorials: proper way to interpret/evaluate?

Question

Sorry for asking, but after watching videos, I’m not sure what is proper way to count double factorials. Is it first or second way?

1st way: $3!! = 1 \cdot 3 = 3$
2nd way: $3!! = (3!)! = 6! = 720$

Answer 1

If you're encountering this in a factorial setting, then it's the second way:

$$n!! \text{ means } (n!)!$$

So, in your example, yes, you would have:

$$3!! = (3!)! = (6)! = 6! = 720$$

But! Beware that you are not actually encountering the double factorial symbol at the aforelinked wikipage.