|Journal of Integer Sequences, Vol. 3 (2000), Article 00.2.1|
Abstract: When the Hankel matrix formed from the sequence 1, a1, a2, ... has an LDLT decomposition, we provide a constructive proof that the Stieltjes matrix SL associated with L is tridiagonal. In the important case when L is a Riordan matrix using ordinary or exponential generating functions, we determine the specific form that SL must have, and we demonstrate, constructively, a one-to-one correspondence between the generating function for the sequence and SL. If L is Riordan when using ordinary generating functions, we show how to derive a recurrence relation for the sequence.
(Concerned with sequences A000108, A000166, A000957, A000984, A001003, A001850, A002426, A005773, A006318, A054912)
Received May 15, 1999; published in Journal of Integer Sequences June 4, 2000.