  The study of sequences of polynomials satisfying high order recurrence
relations is connected with the asymptotic behavior of multiple orthogonal
polynomials, the convergence properties of type II Hermite-Pad\'e
approximation, and eigenvalue distribution of banded Toeplitz matrices. We
present some results for the case of recurrences with constant coefficients
which match what is known for the Chebyshev polynomials of the first kind. In
particular, under appropriate assumptions, we show that the sequence of
polynomials satisfies multiple orthogonality relations with respect to a
Nikishin system of measures.
