Staircase Walk -- from Wolfram MathWorld

via mathworld.wolfram.com

The number of staircase walks on a grid with m horizontal lines and n vertical lines is given by
(m+n; m)=((m+n)!)/(m!n!)

(Vilenkin 1971, Mohanty 1979, Narayana 1979, Finch 2003). The first few values for m=n=1, 2, ..., are 1, 2, 6, 20, 70, 252, ... (Sloane's A000984), which are the central binomial coefficients. A Dyck path is a staircase walk from (0,0) to (n,n) which never crosses (but may touch) the diagonal y=x.

SEE ALSO: Catalan Number, Central Binomial Coefficient, Dyck Path, Ferrers Diagram, Staircase Polygon

Posted via web from jamil's posterous