Schröder number
In mathematics, the Schröder number S n , {\displaystyle S_{n},} also called a large Schröder number or big Schröder number, describes the number of lattice paths from the southwest corner ( 0 , 0 ) {\displaystyle (0,0)} of an n × n {\displaystyle n\times n} grid to the northeast corner ( n , n ) , {\displaystyle (n,n),} using only single steps north, ( 0 , 1 ) ; {\displaystyle (0,1);} northeast, ( 1 , 1 ) ; {\displaystyle (1,1);} or east, ( 1 , 0 ) , {\displaystyle (1,0),} that do not rise above the SW–NE diagonal. The first few Schröder numbers are 1, 2, 6, 22, 90, 394, 1806, 8558, ...