A staircase walk is a lattice path using only unit steps to the right and upward. For nonnegative integers and , the number of such walks from to is given by
(Vilenkin 1971, Mohanty 1979, Narayana 1979, Finch 2003). The first few values for , 1, 2, ..., are 1, 2, 6, 20, 70,
252, ... (OEIS A000984), which are the central
binomial coefficients. A Dyck path is a staircase
walk from
to which stays on or below the diagonal.
and 
, the number of such walks from 
to 
is given by
, 1, 2, ..., are 1, 2, 6, 20, 70,
252, ... (OEIS A000984), which are the central
binomial coefficients. A Dyck path is a staircase
walk from 
to 
which stays on or below the diagonal 
.
