  The paper is concerned with a sequence of constants which appear in several
problems. These problems include the minimal eigenvalue of certain positive
definite Toeplitz matrices, the minimal eigenvalue of some higher-order
ordinary differential operators, the norm of the Green kernels of these
operators, the best constant in a Wirtinger-Sobolev inequality, and the
conditioning of a special least squares problem. The main result of the paper
gives the asymptotics of this sequence.
