Abstract :
In this paper we prove new identities in the Catalan triangle whose (n,p) entry is defined by
Bn,p := p
n
2n
n− p
, n,p ∈ N, p n.
In fact, we show some new identities involving the well-known Catalan numbers, and specially the identity
i
p=1
Bn,pBn,n+p−i(n+ 2p −i) = (n+ 1)Cn
2(n −1)
i −1
, i n,
that appears in a problem related with the dynamical behavior of a family of iterative methods applied to quadratic polynomials.
© 2007 Elsevier Inc. All rights reserved.
