Journal of Integer Sequences, Vol. 4 (2001), Article 01.1.2 |
Email address: wwoan@howard.edu
Abstract: Let H be the Hankel matrix formed from a sequence of real numbers S = {a_0 = 1, a_1, a_2, a_3, ...}, 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 = {d_0 = 1, d_1, d_2, d_3, ...} 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.)