The Hankel Transform ofq-Noncentral Bell Numbers

International Conference on

The Hankel transform of an integer sequence (an) is defined as a sequence formed by the determinants of the matrices An, where An is the upper-left submatrix of size n× n of the Hankel matrix A =  a0 a1 a2 a3 · · · a1 a2 a3 a4 · · · a2 a3 a4 a5 · · · .. .. .. .. . . .  . In this talk, methods in deriving the Hankel transform of Bell and other Bell-type numbers will be discussed, particu...

The Hankel transform

Transformations Preserving the Hankel Transform

Transformations Preserving the Hankel Transform Christopher French Department of Mathematics and Statistics Grinnell College Grinnell, IA 50112 USA [email protected] Abstract We classify all polynomial transformations of integer sequences which preserve the Hankel transform, thus generalizing examples due to Layman and Spivey & Steil. We also show that such transformations form a group ...

The Hankel Transform of the Sum of Consecutive Generalized Catalan Numbers

X iv :m at h/ 06 04 42 2v 1 [ m at h. C O ] 1 9 A pr 2 00 6 The Hankel Transform of the Sum of Consecutive Generalized Catalan Numbers Predrag Rajković, Marko D. Petković, University of Nǐs, Serbia and Montenegro Paul Barry School of Science, Waterford Institute of Technology, Ireland Abstract. We discuss the properties of the Hankel transformation of a sequence whose elements are the sums of c...

Generalized Near-Bell Numbers

The nth near-Bell number, as defined by Beck, enumerates all possible partitions of an n-multiset with multiplicities 1, 1, 1, . . . , 1, 2. In this paper we study the sequences arising from a generalization of the near-Bell numbers, and provide a method for obtaining both their exponential and their ordinary generating functions. We derive various interesting relationships amongst both the gen...