  The Racah algebra $R(n)$ of rank $(n-2)$ is obtained as the commutant of the
\mbox{$\mathfrak{o}(2)^{\oplus n}$} subalgebra of $\mathfrak{o}(2n)$ in
oscillator representations of the universal algebra of $\mathfrak{o}(2n)$. This
result is shown to be related in a Howe duality context to the definition of
$R(n)$ as the algebra of Casimir operators arising in recouplings of $n$ copies
of $\mathfrak{su}(1,1)$. These observations provide a natural framework to
carry out the derivation by dimensional reduction of the generic
superintegrable model on the $(n-1)$ sphere which is invariant under $R(n)$.
