A class of conjectured series representations for .
A common generating function for Catalan numbers and other integer sequences.
A natural extension of Catalan numbers.
A note on a one-parameter family of Catalan-like numbers.
A recursive formula for the Kolakoski sequence A000002.
A slow-growing sequence defined by an unusual recurrence.
Abundancy “outlaws” of the form .
Abundant numbers and the Riemann hypothesis.
Aliquot sequence 3630 ends after reach 100 digits.
An improved estimate concerning 3n+1 predecessor sets
Closed-form expression for Hankel determinants of the Narayana polynomials
We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana...
Derived sequences.
Further results on derived sequences.
Hyper-sums of powers of integers and the Akiyama-Tanigawa matrix.
Increasing integer sequences and Goldbach's conjecture
Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elements in the sequence. The paper introduces and compares several of these classes of sequences, discussing recurrence relations, enumerative problems and questions concerning shortest sequences.
Jumping sequences.
New prime gaps between and .
Notes on a family of Riordan arrays and associated integer Hankel transforms.
On a generalization of the Narayana triangle.
On a number pyramid related to the binomial, Deleham, Eulerian, MacMahon and Stirling number triangles.