A unified approach to some recurrence sequences via Faà di Bruno’s formula

The well-known Faà di Bruno formula for higher derivatives of a composite function plays an important role in combinatorics. In this paper we obtain a unified approach to some recurrence sequences for the complete Bell polynomials by using Faà di Bruno’s formula. Furthermore, we obtain an inverse relation of Lah numbers of two types, and by using this relation we obtain some new and interesting combinatorial identities.