The number of staircase walks on a grid with horizontal lines and vertical lines is given by
(Vilenkin 1971, Mohanty 1979, Narayana 1979, Finch 2003). The first few values for , 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 never crosses (but may touch)
the diagonal .
horizontal lines and 
vertical lines is given by
, 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 never crosses (but may touch)
the diagonal 
.
