## Motzkin numbers of higher rank: generating function and explicit expression

### Summary

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

### Keywords/Phrases

Motzkin number, Catalan number, recursion relation, generating function