Journal of Integer Sequences, Vol. 21 (2018), Article 18.7.5

Motzkin Numbers: an Operational Point of View


M. Artioli
ENEA — Bologna Research Center
Via Martiri di Monte Sole, 4
40129 Bologna
Italy

G. Dattoli
ENEA — Frascati Research Center
Via Enrico Fermi 45
00044 Frascati, Rome
Italy

S. Licciardi
Dept. of Mathematics and Computer Science
University of Catania
Viale A. Doria 6
95125, Catania
Italy
and
ENEA — Frascati Research Center
Via Enrico Fermi 45
00044 Frascati, Rome
Italy

S. Pagnutti
ENEA — Bologna Research Center
Via Martiri di Monte Sole, 4
40129, Bologna
Italy

Abstract:

The Motzkin numbers can be derived as coefficients of hybrid polynomials. Such an identification allows the derivation of new identities for this family of numbers, and offers a tool to investigate previously unnoticed links with the theory of special functions and with the relevant treatment in terms of operational means. The use of umbral methods opens new directions for further developments and generalizations, which leads, e.g., to the identification of new Motzkin-associated forms.

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(Concerned with sequences A000217 A000910 A001470 A014531 A014532 A034827 A050534 A052501 A118934 A240440.)

Received February 26 2018; revised versions received May 16 2018; June 2 2018; August 25 2018. Published in Journal of Integer Sequences, August 26 2018.

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