Step 1: Write the parents' genotypes.
The father is blood group A and homozygous, so his genotype is $ I^A I^A $. The mother is blood group O, so her genotype is $ ii $.
Step 2: Find the gametes.
The father can give only $ I^A $ in every sperm. The mother can give only $ i $ in every egg.
Step 3: Make the cross.
Combining the gametes, every child gets one $ I^A $ from father and one $ i $ from mother. So each child is $ I^A i $.
Step 4: Read the child's blood group.
Since $ I^A $ is dominant over $ i $, the genotype $ I^A i $ shows blood group A. So all children are blood group A.
Step 5: List which groups cannot appear.
Because the only possible group is A, the children can never be B or AB.
Step 6: Match to the option asking what is NOT expected.
The question asks which set is not expected. Since groups B and AB can never appear, the not-expected set listed is B, AB, A.
\[ \boxed{\text{B, AB, A}} \]