Note that B(n) is the n Bell number while S(n, k) is the Stirling number of the second kind. We have translated Spiveyâ€™s notation into Riordanâ€™s familiar notation which we find more preferable in ourâ€¦ (More)

By iterating (0.2), f(n + r) can be written as a linear combination of binomial coefficients with polynomial coefficients Arj(n), 0 â‰¤ j â‰¤ r âˆ’ 1. The polynomials Arj(n) have various interestingâ€¦ (More)

Let (b n) nâ‰¥0 be the binomial transform of (a n) nâ‰¥0. We show how a binomial transformation identity of Chen proves a symmetrical Bernoulli number identity attributed to Carlitz. We then modifyâ€¦ (More)

It is well-known that the Bell numbers {B(n)}n=0 have exponential generating function âˆ‘âˆž n=0 B(n) x n! = exp(e xâˆ’1), which satisfies the differential equation d dxg(x) = exg(x). In this paper, weâ€¦ (More)

Here presented are the definitions of (c)-Riordan arrays and (c)-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials. The characterization of (c)-Riordan arraysâ€¦ (More)

We study two sums involving the Stirling numbers and binomial coefficients. We find their closed forms, and discuss the connection between these sums. Dedicated to the memory of our mentors,â€¦ (More)