2 problems

Let $A^{(s)}(n)$ be the generalized Franel numbers, let $A^{(s)}_1(n)$ denote the first auxiliary sequence arising from the expansion used to obtain the Apéry limits, and define ……

Higher Apéry-limit conjecture. For $d\geq 5$, there is a unique such solution $C^{(d)}(n)$ satisfying