Since this is a double factorial, then each term in the multiplication should be a distance of two units away from the neighboring terms.
Perform a change of variable and see if it makes sense:
let 2n+1 = m
m!! = (m - 2)!! * m -> need to be two units away.
Replace the m back:
(2n + 1)!! = (2n + 1 - 2)!! * (2n + 1)
= (2n - 1)!! * (2n + 1)
So... Yes you're correct.