Congruences for Catalan-Larcombe-French numbers

Xiao-Juan Ji, Zhi-Hong Sun

Let $\{P_n\}$ be the Catalan-Larcombe-French numbers given by $P_0=1,P_1=8$ and $n^2{P}_n=8(3n^2-3n+1)P_{n-1}-128(n-1{)}^2{P}_{n-2}$ $(n\ge 2)$, and let $S_n=P_n/2^n$. In this paper we…