8 problems

Let $A$ and $D$ denote the Eulerian and Delannoy triangles, respectively, and let $A^2$ and $D^2$ be their matrix squares. For a lower triangular matrix $M$, write its $n$-th row g…

Let $D_n$ and $S_n$ denote the Delannoy and Schröder numbers, respectively, defined by … Let $p>3$ be a prime. Sun's supercongruence. … This congruence was raised by Z.-W. Sun in 2…

Let $a(n)=\sum_{0\leq i\leq n}\binom{n}{i}\binom{n+i}{i}$ be the central Delannoy number, and let $b(n)=\nu_3(a(n))$. Shallit's central Delannoy valuation conjecture. The sequence…

Let $p>3$ be a prime, and let $D_k$ and $S_k$ denote the central Delannoy and large Schröder numbers, respectively. Let $E_j$ denote the Euler numbers. Sun's conjecture. Sun conjec…

Let … where $D_0,D_1,\ldots$ are the central Delannoy numbers. Zhi-Wei Sun's conjecture. The number $a(n)$ is an integer for every positive integer $n$. The source says that Sun pr…

Let $p$ be a prime satisfying $p\equiv 2\pmod 3$. Let $T_k(3,3)$ and $M_k(3,3)$ denote the specialized sequences used in the paper. The author's conjecture. One has … This strength…

Let $d_k(x)$ and $s_k(x)$ be the two Delannoy-related polynomials considered in the paper. Integer-valued Delannoy-polynomial power conjecture. For all positive integers $m$ and…

For positive integers $m,n,r$, let $D_q(m,k)$ and $D_{q^{-1}}(m,k)$ be the natural $q$-Delannoy numbers defined by … with…