Catalan numbers and Schubert polynomials for $w=1(n+1)... 2$
  We show that the Schubert polynomial S_w specializes to the Catalan number C_n when $w=1(n+1)...2$. Several proofs of this result as well as a q-analog are given. An application to the singularities of Schubert varieties is given. 
Alexander Woo