  Higher-order perturbative calculations in Quantum (Field) Theory suffer from
the factorial increase of the number of individual diagrams. Here I describe an
approach which evaluates the total contribution numerically for finite
temperature from the cumulant expansion of the corresponding observable
followed by an extrapolation to zero temperature. This method (originally
proposed by Bogolyubov and Plechko) is applied to the calculation of
higher-order terms for the ground-state energy of the polaron. Using
state-of-the-art multidimensional integration routines 2 new coefficients are
obtained corresponding to a 4- and 5-loop calculation.
