Geodesic
Motzkin numbers of higher rank: generating function and explicit expression
Journal of integer sequences, Tome 10 (2007) no. 7
The generating function for the (colored) Motzkin numbers of higher rank introduced recently is discussed. C onsidering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given. Some explicit expressions are given for the higher rank case in the first few instances.
Classification : 05A15, 11B37, 11B83
Keywords: Motzkin number, Catalan number, recursion relation, generating function 
@article{JIS_2007__10_7_a2,
     author = {Mansour,  Toufik and Schork,  Matthias and Sun,  Yidong},
     title = {Motzkin numbers of higher rank: generating function and explicit expression},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {7},
     zbl = {1141.05308},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_7_a2/}
}
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Mansour,  Toufik; Schork,  Matthias; Sun,  Yidong. Motzkin numbers of higher rank: generating function and explicit expression. Journal of integer sequences, Tome 10 (2007) no. 7. http://geodesic.mathdoc.fr/item/JIS_2007__10_7_a2/