Symmetries in Steinhaus triangles and in generalized Pascal triangles.
Tabulka binomických koefficientů
The Akiyama-Tanigawa algorithm for Carlitz's -Bernoulli numbers.
The Euler series transformation and the binomial identities of Ljunggren, Munarini and Simons.
The function and some well-known sequences.
The -binomial transforms and the Hankel transform.
The Kazandzidis supercongruences. A simple proof and an application
The Lagrange inversion formula and divisibility properties.
The last digit of and .
The number of binomial coefficients in residue classes modulo p and .
The number of topologies on a finite set.
The p-adic valuation of k-central binomial coefficients
Transforming recurrent sequences by using the binomial and invert operators.
Triangular numbers in geometric progression.
Truncating binomial series with symbolic summation.
Truncations of Gauss' square exponent theorem
We establish two truncations of Gauss’ square exponent theorem and a finite extension of Euler’s identity. For instance, we prove that for any positive integer , where
Two -identities from the theory of fountains and histograms proved with a tri-diagonal determinant.
Two very short proofs of combinatorial identity.
Unification of the quintuple and septuple product identities.
Unimodal rays in the regular and generalized Pascal pyramids.