  We consider a connected negative definite plumbing graph, and we assume that
the associated plumbed 3-manifold is a rational homology sphere. We provide two
new combinatorial formulae for the Seiberg-Witten invariant of this manifold.
The first one is the constant term of a `multivariable Hilbert polynomial', it
reflects in a conceptual way the structure of the graph, and emphasizes the
subtle parallelism between these topological invariants and the analytic
invariants of normal surface singularities. The second formula realizes the
Seiberg-Witten invariant as the normalized Euler characteristic of the lattice
cohomology associated with the graph, supporting the conjectural connections
between the Seiberg-Witten Floer homology, or the Heegaard-Floer homology, and
the lattice cohomology.
