  In this note, we present the result for the QCD corrections to the decay of
the Higgs boson into two photons in the large-$\beta_0$ limit of QCD, providing
the first two terms in the heavy-top expansion. From our results, one can
easily read off the exact leading-$n_f$ QCD contributions in analytic form to
all orders in the strong coupling, $\alpha_s$, where $n_f$ is the number of
massless quarks, and identify the leading renormalon singularities. We give
explicit results for the leading-$n_f$ coefficients at 6 and 7 loops and use
the large-$\beta_0$ result to speculate about the size of yet unknown (but
small) higher-order contributions to the QCD series.
