A Lattice Path from one point to another is -good if it lies completely below the line

Hilton and Pederson (1991) show that the number of -good paths from (1, ) to (, ) under the condition is

where is a Binomial Coefficient, and

where is the Floor Function.

**References**

Hilton, P. and Pederson, J. ``Catalan Numbers, Their Generalization, and Their Uses.'' *Math. Intel.* **13**, 64-75, 1991.

© 1996-9

1999-05-26