Two explicit formulas for the generalized Motzkin numbers

Abstract

Abstract In the paper, by the Faà di Bruno formula, the authors establish two explicit formulas for the Motzkin numbers, the generalized Motzkin numbers, and the restricted hexagonal numbers.

Keywords

• explicit formula
• Motzkin number
• generalized Motzkin number
• restricted hexagonal number
• Catalan number
• generating function