Sum-Difference Sequences and Catalan Numbers

 Let be a sequence of natural numbers > 1, and set . The sequence is called admissible if a _i divides for all i. It is known that the admissible sequences are counted by the Catalan numbers. We present a proof of this fact which, in turn, leads to some interesting combinatorial and number-theoretic questions. Received 12 May 1997; in revised form 9 June 1997