We have computed by a Monte Carlo method the fourth virial coefficient
of free anyons, as a function of the statistics angle theta. It can b
e fitted by a four term Fourier series, in which two coefficients are
fixed by the known perturbative results at the boson and fermion point
s. We compute partition functions by means of path integrals, which we
represent diagrammatically in such a way that the connected diagrams
give the cluster coefficients. This provides a general proof that all
cluster and virial coefficients are finite. We give explicit polynomia
l approximations for all path integral contributions to all cluster co
efficients, implying that only the second virial coefficient is statis
tics dependent, as is the case for two-dimensional exclusion statistic
s. The assumption leading to these approximations is that the tree dia
grams dominate and factorize.