2 problems

Let $S_{0,n}$ denote the super Catalan numbers with $m=0$, and consider the directed graphs constructed in Definition. Caldwell et al.'s conjecture. These graphs are generalized ac…

Let $S(m,n)$ denote the super Catalan numbers … For an odd prime $p$, let $\left(\frac{p}{3}\right)$ denote the Legendre symbol. Apagodu's conjecture. For any odd prime $p$, … and…