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In this paper, we deal with several combinatorial sums and some infinite series which involve the reciprocals of binomial coefficients. Many binomial identities as well as some polynomial identities are proved.

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)

In this paper, the authors establish some identities involving inverses of binomial coefficients and generalize an identity.

- Fengzhen Zhao, Tianming Wang
- 1999

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)

In this article, we study the generalized Bernoulli and Euler polyno-mials, and obtain relationships between them, based upon the technique of matrix representation.