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