Series of Multiplying Odd Numbers Involving Factorials?

So for a bonus question, my teacher asked anyone if they could figure out how to write an equation for the following:

So basically it's the summation from to of plugging into an equation and then getting an odd number and then by plugging in every number less than you will get the multiplication of an odd number and every odd number less than it until 1. Does that make sense? It's kind of like a factorial but only multiplying odd numbers.

Anyways, I think I kind of figured it out but I'm not too sure because I'm not really familiar with the rules of factorials, but here's what I came up with:

But I'm not sure if that means

which would result in something like if I plug in .

OR...if it means

which would result in something like if was plugged in.

Sooo...if anyone actually read all of this and can tell me whether my final equation of is correct or not and if not then how can I can fix it then I would be so appreciative and would give you a cookie...if I had one!(Giggle) Seriously though...thank you so much to whoever helps!

Re: Series of Multiplying Odd Numbers Involving Factorials?

Thank you Chris L. I was so close to figuring this out myself.. Sigh.. Thanks for your help