  Jacobi polynomials are polynomials whose zeros form the unique solution of
the Bethe Ansatz equation associated with two sl_2 irreducible modules. We
study sequences of r polynomials whose zeros form the unique solution of the
Bethe Ansatz equation associated with two highest weight sl_{r+1} irreducible
modules, with the restriction that the highest weight of one of the modules is
a multiple of the first fundamental weight. We describe the recursion which can
be used to compute these polynomials. Moreover, we show that the first
polynomial in the sequence coincides with the Jacobi-Pi\~neiro multiple
orthogonal polynomial and others are given by Wronskian type determinants of
Jacobi-Pi\~neiro polynomials. As a byproduct we obtain a counterexample to the
Bethe Ansatz Conjecture for the Gaudin model.
