Congruences modulo arbitrary powers of $5$ and $7$ for Andrews and Paule's partition diamonds with $(n+1)$ copies of $n$

Julia Q. D. Du, Olivia X. M. Yao

Recently, Andrews and Paule introduced a partition function $PDN1(N)$ which denotes the number of partition diamonds with $(n+1)$ copies of $n$ where summing the parts at the links…