  The parametrized black hole quasinormal ringdown formalism is useful to
compute quasinormal mode (QNM) frequencies if a master equation for the
gravitational perturbation around a black hole has a small deviation from the
Regge-Wheeler or Zerilli equation. In this formalism, the deviation of QNM
frequency from general relativity can be calculated by small deviation
parameters and model independent coefficients. In this paper, we derive
recursion relations for the model independent coefficients. Using these
relations, the higher order coefficients are written only by the lower order
coefficients. Thus, we only need the lower order coefficients when we
numerically compute the model independent coefficients.
