If a man with blood type A, one of whose parents had blood type O, marries a woman with blood type AB, what are the putative genotypes of the offspring?

If the man has blood type A one of whose parents had blood type O then he must be having the genotype IAi and the woman with blood group AB would have genotype IAIB. So if they produce offspring than the putative genotype of the offspring would be IAIA, IAi, IAIB, and IBi.

IA i

IA IAIA IAi

IB IAIB IBi

Therefore out of four offspring, two offspring would be having A blood group, one offspring would have AB blood group and one offspring would have B blood group.