The a rationibus was the secretary of finance for the Roman Empire, in charge of maintaining the accounts and expenditures of the fiscus which was the imperial treasury. This official's role in the finances of the Early Empire was considerable. The office was originally held by a freedman, but from the 2nd century AD (around the reigns of Trajan and Hadrian), only Equestrians (Equites) occupied this position after the reputation of freedmen had been blackened due to their undue influence at the imperial court in which corruption and bribery played a big role. The office of the a rationibus was abolished due to Diocletian's tetrarchic reforms by which the comes sacrarum largitionum (master of the sacred largess) became head of the imperial financial chests during the 4th and 5th century AD.
Freedmen who held the office of a rationibus are Pallas, Phaon, and Etruscus Pater.
For more on the freedmen at court, see P. Weaver, Familia Caesaris. A Study of the Emperor’s Freedmen and Slaves, Cambridge, 1979.