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A technique used by André (1887) to provide an elegant solution to the Ballot Problem (Hilton and Pederson 1991).
References
André, D. ``Solution directe du problème résolu par M. Bertrand.'' Comptes Rendus Acad. Sci. Paris
105, 436-437, 1887.
Comtet, L. Advanced Combinatorics. Dordrecht, Netherlands: Reidel, p. 22, 1974.
Hilton, P. and Pederson, J. ``Catalan Numbers, Their Generalization, and Their Uses.'' Math. Intel. 13, 64-75, 1991.
Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 185, 1991.