Successive Derivatives and Integer Sequences

Non-Abelian Sequenceable Groups Involving ?-Covers

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

Rings of functions with integer derivatives at x=1

Integer Sequences Connected with Extensions of the Bell Polynomials

The Encyclopedia of Integer Sequences includes some sequences that are connected with the Bell numbers and that have a particular combinatorial meaning. In this article, we find a general meaning for framing sequences, including the above mentioned ones. Furthermore, by using Laguerre-type derivatives, we derive the Laguerre-type Bell numbers of higher order, showing, as a by-product, that it i...

A Combinatorial Interpretation for Certain Relatives of the Conolly Sequence

For any integer s ≥ 0, we derive a combinatorial interpretation for the family of sequences generated by the recursion (parameterized by s) hs(n) = hs(n − s − hs(n − 1)) + hs(n − 2− s − hs(n − 3)), n > s + 3, with the initial conditions hs(1) = hs(2) = · · · = hs(s+2) = 1 and hs(s+3) = 2. We show how these sequences count the number of leaves of a certain infinite tree structure. Using this int...

The role of binomial type sequences in determination identities for Bell polynomials

Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and binomial type sequences in first part, and, we generalize the results obtained in [4] in second part.