The Schröder number is the number of Lattice Paths in the Cartesian plane that start at
(0, 0), end at , contain no points above the line , and are composed only of steps (0, 1), (1, 0), and (1,
1), i.e., , , and . The diagrams illustrating the paths generating , , and
are illustrated above. The numbers are given by the Recurrence Relation
See also Binomial Coefficient, Catalan Number, Delannoy Number, Lattice Path, Motzkin Number, p-Good Path
Sloane, N. J. A. Sequence
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.