  It has been demonstrated both theoretically and experimentally that genuine
multipartite entanglement between qubits can exist even in the absence of
multipartite correlations. Here we provide first examples of this effect in
higher dimensional systems -- qudits. We construct states in which genuine
$N$-partite entanglement between qudits is supported only by correlations
involving strictly less than $N$ particles. The construction differs in several
aspects from the ones for qubits. The states introduced here are a natural
test-bed for candidate quantifiers of genuinely multipartite quantum
correlations.
