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.