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)
BACKGROUND Many proposed statistical measures can efficiently compare protein sequence to further infer protein structure, function and evolutionary information. They share the same idea of using k-word frequencies of protein sequences. Given a protein sequence, the information on its related protein sequences hasn't been used for protein sequence… (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.
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)