I believe your right...no father. BHO Sr is an adopted father.
BHO Sr is probably the biological father, but not listed on the birth certificate. Making him a B-tard.
It is possible that someone else fathered him, some suspect Frank Marshall. I’d say this is not probable, but Marshall was a mentor and was a Commie. He was also a pedophile, and could have also known Stanley.
We know that BHO Jr. stated in his book that his mother had a “thing” for black men, and this complicated his understanding of her Black/White race relationship.