“Catalan traffic” and integrals on the Grassmannian of lines

We prove that certain numbers occurring in a problem of paths enumeration, studied by Niederhausen in [Catalan traffic at the beach, Eletron. J. Combin. 9 (R33) (2002) 1–17] (see also [R.P. Stanley, Catalan addendum, version of 30 October 2005. 〈〈http://www-math.mit.edu/∼∼rstan/ec/catadd.pdf〉〉]), are top intersection numbers in the cohomology ring of the Grassmannian of the lines in the complex projective (n+1)(n+1)- space.