Geodesic
Motzkin numbers, central trinomial coefficients and hybrid polynomials
Journal of integer sequences, Tome 11 (2008) no. 1
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.
Classification : 11B83, 05A19, 33C45
Keywords: central trinomial coefficients, Motzkin numbers, Hermite-kampé de fériét polynomials 
@article{JIS_2008__11_1_a4,
     author = {Blasiak,  P. and Dattoli,  G. and Horzela,  A. and Penson,  K.A. and Zhukovsky,  K.},
     title = {Motzkin numbers, central trinomial coefficients and hybrid polynomials},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {1},
     zbl = {1165.11027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_1_a4/}
}
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%0 Journal Article
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%A Penson,  K.A.
%A Zhukovsky,  K.
%T Motzkin numbers, central trinomial coefficients and hybrid polynomials
%J Journal of integer sequences
%D 2008
%V 11
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%G en
%F JIS_2008__11_1_a4
Blasiak,  P.; Dattoli,  G.; Horzela,  A.; Penson,  K.A.; Zhukovsky,  K. Motzkin numbers, central trinomial coefficients and hybrid polynomials. Journal of integer sequences, Tome 11 (2008) no. 1. http://geodesic.mathdoc.fr/item/JIS_2008__11_1_a4/