What Legal Rights Might A Biological Father Have To A Child Born In The U.s. But Residing In Europe?

I'm currently pregnant but do not have a relationship with the biological father, nor do I plan to inform him about the pregnancy at this time or list him on the birth certificate. I'm Permanent Resident/Green Card holder and may move back to Europe within the next year, or once the child is at least six months old. If I decide to inform the biological father in the future (after relocating to back to Europe), what legal rights might he have? The child will have dual citizenship in both the U.S. and X European Country.