  We compute the Hilbert series of the complex Grassmannian using invariant
theoretic methods and show that its h-polynomial coincides with the k-Narayana
polynomial. We give a simplified formula for the h-polynomial of Schubert
varieties. Finally, we use a generalized hypergeometric Euler transform to find
simplified formulae for the k-Narayana numbers, i.e. the h-polynomial of the
Grassmannian.
