  We performed Monte Carlo simulations of the two-dimensional q-state Potts
model with q=10, 15, and 20 to study the energy and magnetization cumulants in
the ordered and disordered phase at the first-order transition point $\beta_t$.
By using very large systems of size 300 x 300, 120 x 120, and 80 x 80 for q=10,
15, and 20, respectively, our numerical estimates provide practically (up to
unavoidable, but very small statistical errors) exact results which can serve
as a useful test of recent resummed large-q expansions for the energy cumulants
by Bhattacharya `et al.' [J. Phys. I (France) 7 (1997) 81]. Up to the third
order cumulant and down to q=10 we obtain very good agreement, and also the
higher-order estimates are found to be compatible.
