Abstract
The Catalan number C n is defined to be 2n n (n+1) . One of its occurrences is as the number of ways of bracketing a product of n+1 terms taken from a set with binary operation. In this note the corresponding result for a set with a k-ary operation is considered. A combinatorial proof is given which does not involve generating functions or inversion formulae. The result is further generalised to obtain a simpler proof of a formula of Erdelyi and Etherington [2], interpreted here as a result concerning a set with several k i -ary operations.
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