Mansour, Toufik; Schork, Matthias; Sun, Yidong

Motzkin numbers of higher rank: generating function and explicit expression

J. Integer Seq. 10(7), Article 07.7.4, 11 p., electronic only (2007)


Summary: 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.

Mathematics Subject Classification

05A15, 11B37, 11B83


Motzkin number, Catalan number, recursion relation, generating function