My understanding of inherited citizenship is that it does not depend on the marital status of the parents. As long as the father has recognized the child and his name is on the birth certificate, he is considered the father according to the NBC definition. “...of parents who are citizens” it says in Vattel, not “of married parents who are citizens.” As long as Obama Senior’s name is on the birth certificate, he is a parent as per Vattel’s NBC definition.