Riordan matrices and sums of harmonic numbers

We obtain a general identity involving the row-sums of a Riordan matrix and the harmonic numbers. From this identity, we deduce several particular identities involving numbers of combinatorial interest, such as generalized Fibonacci and Lucas numbers, Catalan numbers, binomial and trinomial coefficients and Stirling numbers

Infinite series identities involving quadratic and cubic harmonic numbers

By means of the modified Abel lemma on summation by parts, we investigate infinite series involving quadratic and cubic harmonic numbers. Several infinite series identities are established for π 2 and ζ(3) as consequences

Euler-related sums

The purpose of this paper is to develop a set of identities for Euler type sums of products of harmonic numbers and reciprocal binomial coefficients