Application of Faà di Bruno's Formula in the Construction of Combinatorial Identities

摘要

Chou, Hsu, and Shiue in [3] use Faà di Bruno's formula give a class of composite series expansions. In this paper, we apply those expansions to construct a class of identities for Catalan numbers, large Schroder numbers, small Schroder numbers, parametric Catalan numbers, Stirling numbers, binomial numbers, some other recursive number sequences, and recursive polynomial sequences.