You can't make a hen go broody, but if you have one that you know is prone to broodiness you could probably encourage it by giving her some eggs to sit on. Your hen doesn't sound broody, just normal. Most of my hens all have their favourite places to lay, but they only sit around for maybe half an hour at a time, apart from one loud old witch who sits cackling at top volume for ninety minutes each day. Any longer than that, and you can suspect broodiness...
Oh, and 15-20 eggs is a bit much to expect a hen to cover. A dozen at most would be reasonable...