Recent serological studies of seasonal influenza A in humans suggest a striking characteristic profile of immunity against age, which holds across different countries and against different subtypes of influenza. For both H1N1 and H3N2, the proportion of the population seropositive to recently circulated strains peaks in school-age children, reaches a minimum between ages 35-65, then rises again in the older ages. This pattern is little understood. Variable mixing between different age classes can have a profound effect on disease dynamics, and is hence the obvious candidate explanation for the profile, but using a mathematical model of multiple influenza strains, we see that age dependent transmission based on mixing data from social contact surveys cannot on its own explain the observed pattern. Instead, the number of seropositive individuals in a population may be a consequence of 'original antigenic sin'; if the first infection of a lifetime dominates subsequent immune responses, we demonstrate that it is possible to reproduce the observed relationship between age and seroprevalence. We propose a candidate mechanism for this relationship, by which original antigenic sin, along with antigenic drift and vaccination, results in the age profile of immunity seen in empirical studies.