  We study the operad $n\text{-}Lie_d$, whose algebras are graded $n$-Lie
algebras with degree $d$ $n$-arity operations, which were introduced in Nambu
mechanics and later studied in the algebraic setting with Filippov. We compute
the Koszul dual of $n\text{-}Lie_d$, called $n\text{-}Com_{-d+n-2}$, whose
relations are derived from the Specht module $S^{(n,n-1)}$ for a partition
$(n,n-1)$ of $2n-1$. The intrinsic connection between these two operads come
from the eigenvalues of the sequence of graphs $\{\mathcal{O}_n\}_{n\geq 0}$,
called the Odd graphs, whose spectrum is related to the lower triangular
sequence $\{\mathcal{E}_{r,n}\}$, called the Catalan triangle.
