I suppose it depends on what "rights" means as well as if the child wants a relationship with his or her father. Clearly a child over the age of 12 can decide if they want to pursue the opportunity. As long as the mother hasn't posioned the child against their father he or she can make up their own mind in a fair way.
You have to also take into account what is motivating the sudden interest. Did he find religion? Is he dying? Has his life turned around in some significant way.? Has he matured?...etc People do evolve or grow overtime and it's not fair to lock them into a box forever based upon something they did or said several years ago. They should be allowed to make amends.
Sometimes it's the ex who is still upset with the father or he makes things uncomfortable whenever he is around her and her new husband/significant other.
Needless to say every child is entitled to get to know their father especially if he's making an effort to see them unless he is dangerous. It takes both the egg and the sperm to make a "specific child". Another man could not have produced that "same child". Whether a woman hates her ex or not the child she loves is here in part because of his genetic seed. Without him or their past together (this child) would not be here.
One man's opinion! :-)