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In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to c n is an infinite, lower triangular array determined by the pair (g(t), f (t)) and has the generic element d n,k = [t n /c n ]g(t)(f (t)) k /c k , where c n is a fixed sequence of non-zero constants with c 0 = 1. We demonstrate that the generalized(More)
The generalized Fibonacci and Lucas numbers are defined by a n-B n ^ ^ z f-> K = ""+fi n (i) where a = P+ ^ P 2 ~ 4q , (3 = P ~^ P 2 ~ 4q , p > 0, q^O, and p 2-4q > 0. It is obvious that {£/ " } and {VJ are the usual Fibonacci and Lucas sequences {FJ and {LJ when p =-q = l. Recently, for the Fibonacci numbers, Zhang established the following identities in(More)
In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for(More)
BACKGROUND Owing to the rapid expansion of RNA structure databases in recent years, efficient methods for structure comparison are in demand for function prediction and evolutionary analysis. Usually, the similarity of RNA secondary structures is evaluated based on tree models and dynamic programming algorithms. We present here a new method for the(More)