On the cardinality of layers in even-valued $n$-dimensional lattice

In this article, we explicitly calculated terms additional to the main one of cardinality asymptotics of central layers in the $n$-dimensional $k$-valued lattice $E^n_k$ for even $k$ as $n\to\infty$. The main term had been found by V.B. Alekseev for a certain class of posets. The case of odd $k$, which is technically less complicated, was the major focus of our previous work.