That is not normal behavior for a cougar. You are a big guy and unless you were bending over the cat would not think of you as prey. It should have run away, not stayed 20 minutes. It's possible that your only having one leg causes you to move in a way that the cat found odd, but that would actually be in your favor.(Think crazy street person moving erratically, not that I think you do that, but to the cat subtle variations in movement can cause confusion)

Now, here's the bad part. You have children if I remember right. Our cats will fixate on any child under 10 or so if they come on the property. Children exhibit all the signs of prey(small stature, nervous energetic movements, bending over, etc.) Personally, I like cats and all, but I would've shot it. Make sure you contact Fish and Game and have them track it to at least get it out of the neighborhood. Also, is anyone missing any pets in the neighborhood?