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)