  Here we have developed the general parametrization for spherically symmetric
and asymptotically flat black-hole spacetimes in an arbitrary metric theory of
gravity. The parametrization is similar in spirit to the parametrized
post-Newtonian (PPN) approximation, but valid in the whole space outside the
event horizon, including the near horizon region. This generalizes the
continued-fraction expansion method in terms of a compact radial coordinate
suggested by Rezzolla and Zhidenko [Phys.Rev.D 90 8, 084009 (2014)] for the
four-dimensional case. As the first application of our higher-dimensional
parametrization we have approximated black-hole solutions of the
Einstein-Lovelock theory in various dimensions. This allows one to write down
the black-hole solution which depends on many parameters (coupling constants in
front of higher curvature terms) in a very compact analytic form, which depends
only upon a few parameters of the parametrization. The approximate metric
deviates from the exact (but extremely cumbersome) expressions by fractions of
one percent even at the first order of the continued-fraction expansion, which
is confirmed here by computation of observable quantities, such as quasinormal
modes of the black hole.
