## p-Good Path

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.

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