Journal of Integer Sequences, Vol. 4 (2001), Article 01.1.2

Hankel Matrices and Lattice Paths

Wen-Jin Woan
Department of Mathematics
Howard University
Washington, D.C. 20059, USA

Email address: wwoan@howard.edu

Abstract: Let H be the Hankel matrix formed from a sequence of real numbers S = {a₀ = 1, a₁, a₂, a₃, ...}, and let L denote the lower triangular matrix obtained from the Gaussian column reduction of H. This paper gives a matrix-theoretic proof that the associated Stieltjes matrix S_L is a tri-diagonal matrix. It is also shown that for any sequence (of nonzero real numbers) T = {d₀ = 1, d₁, d₂, d₃, ...} there are infinitely many sequences such that the determinant sequence of the Hankel matrix formed from those sequences is T.

(Mentions sequences A000108 A001006 A001850.)