One deals with a certain generalization of the (generic) Hankel matrix. Fixing a fieldK, for a suitable diagonal term order on the polynomial ringBoverKgenerated by the entries of this matrix, one considers theK-subalgebraA⊂Bgenerated by the set of initial terms of the the maximal minors of the matrix. The algebraAdetects the underlying combinatorics in terms of certain generalized standard tableaux and these give a way of showing thatAis normal.Amore involved technique also yields that the Rees algebra of the ideal ofBgenerated by the generators ofAis normal. In particular, both algebras are Cohen-Macaulay. We also present a Gröbner basis for the presentation ideal ofAand compute some numerical invariants using the simplicial complex associated toA.