Journal of Integer Sequences, Vol. 20 (2017), Article 17.10.2

Integer Sequences Connected with Extensions of the Bell Polynomials

Pierpaolo Natalini
Università degli Studi Roma Tre
Dipartimento di Matematica e Fisica
Largo San Leonardo Murialdo, 1
00146 - Roma

Paolo Emilio Ricci
International Telematic University UniNettuno
Corso Vittorio Emanuele II, 39
00186 - Roma


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 is possible to construct new integer sequences which are not included in the Encyclopedia.

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(Concerned with sequences A000326 A005945 A144150.)

Received March 13 2017; revised versions received August 24 2017; September 20 2017. Published in Journal of Integer Sequences, October 29 2017.

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