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 {\displaystyle } of an n × n {\displaystyle n\times n} grid to the northeast corner, {\displaystyle,} using only single steps north, ; {\displaystyle ;} northeast, ; {\displaystyle ;} or east,, {\displaystyle,} that do not rise above the SW–NE diagonal. Wikipedia