Abstract

We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the “ballot sequences”, variant to which Catalan numbers offer a solution.Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined.

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