| Path : /usr/share/calc/help/ |
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NAME
catalan - Catalan number
SYNOPSIS
catalan(n)
TYPES
n integer
return integer
DESCRIPTION
If n >= 0, this returns the Catalan number for index n:
catalan(n) = comb(2*n,n)/(n + 1)
Zero is returned for negative n.
The Catalan numbers occur in solutions of several elementary
combinatorial problems, e.g. for n >= 1, catalan(n) is the number of
ways of using parentheses to express a product of n + 1 letters in
terms of binary products; it is the number of ways of dissecting a
convex polygon with n + 2 sides into triangles by nonintersecting
diagonals; it is the number of integer-component-incrementing paths
from (x,y) = (0,0) to (x,y) = (n,n) for which always y <= x.
EXAMPLE
; print catalan(2), catalan(3), catalan(4), catalan(20)
2 5 14 6564120420
LIMITS
none
LINK LIBRARY
NUMBER *qcatalan(NUMBER *n)
SEE ALSO
comb, fact, perm
## Copyright (C) 2000 Ernest Bowen
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 2000/12/14 01:33:00
## File existed as early as: 2000
##
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/