Motzkin numbers of higher rank: Generating function and explicit expression

Toufik Mansour, Matthias Schork, Yidong Sun

Research output: Contribution to journalArticlepeer-review


The generating function for the (colored) Motzkin numbers of higher rank introduced recently is discussed. Considering 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.

Original languageEnglish
Article number07.7.4
JournalJournal of Inequalities in Pure and Applied Mathematics
Issue number2
StatePublished - 2007


  • Catalan number
  • Generating function
  • Motzkin number
  • Recursion relation

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Motzkin numbers of higher rank: Generating function and explicit expression'. Together they form a unique fingerprint.

Cite this