Journal of Integer Sequences, Vol. 11 (2008), Article 08.1.1

Motzkin Numbers, Central Trinomial Coefficients and Hybrid Polynomials


P. Blasiak
H. Niewodniczański Institute of Nuclear Physics
Polish Academy of Sciences
ul. Eliasza-Radzikowskiego 152
PL 31342 Kraków
Poland

G. Dattoli
ENEA
Dipartimento Innovazione
Divisione Fisica Applicata Centro Ricerche Frascati
Via E. Fermi 45
I 00044 Frascati, Rome
Italy

A. Horzela
H. Niewodniczański Institute of Nuclear Physics
Polish Academy of Sciences
ul. Eliasza-Radzikowskiego 152
PL 31342 Kraków
Poland

K. A. Penson
Laboratoire de Physique Théorique de la Matière Condensée
Universitée Pierre et Marie Curie
CNRS UMR 7600
Tour 24 - 2ième ét.
4 pl. Jussieu
F-75252 Paris Cedex 05
France

K. Zhukovsky
ENEA, Dipartimento Innovazione
Divisione Fisica Applicata Centro Ricerche Frascati
Via E. Fermi 45
I 00044 Frascati, Rome
Italy

Abstract:

We show that the formalism of hybrid polynomials, interpolating between Hermite and Laguerre polynomials, is very useful in the study of Motzkin numbers and central trinomial coefficients. These sequences are identified as special values of hybrid polynomials, a fact which we use to derive their generalized forms and new identities satisfied by them.

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(Concerned with sequences A000085 A001006 A002426 and A115329 .)

Received November 24 2005; revised version received June 5 2006; August 12 2007; January 10 2008. Published in Journal of Integer Sequences, January 13 2008.

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