Journal of Integer Sequences, Vol. 4 (2001), Article 01.1.5

The Hankel Transform and Some of its Properties

John W. Layman
Department of Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061, USA
Email address: layman@math.vt.edu

Abstract: The Hankel transform of an integer sequence is defined and some of its properties discussed. It is shown that the Hankel transform of a sequence S is the same as the Hankel transform of the binomial or invert transform of S. If H is the Hankel matrix of a sequence and H = LU is the LU decomposition of H, the behavior of the first super-diagonal of U under the binomial or invert transform is also studied. This leads to a simple classification scheme for certain integer sequences.

(Concerned with sequences A000079, A000085, A000108, A000110, A000142, A000166, A000178, A000296, A000522, A000957, A000984, A001006, A001405, A001700, A002212, A002426, A003701, A005043, A005425, A005493, A005494, A005572, A005773, A007317, A010483, A010842, A026375, A026378, A026569, A026585, A026671, A033321, A033543, A045379, A049027, A052186, A053486, A053487, A054341, A054391, A054393, A055209, A055878, A055879, A059738.)