  We reinvestigate the correlation between black hole mass and bulge
concentration. With an increased galaxy sample, updated estimates of galaxy
distances, black hole masses, and Sersic indices `n' - a measure of
concentration - we perform a least-squares regression analysis to obtain a
relation suitable for the purpose of predicting black hole masses in other
galaxies. In addition to the linear relation, log(M_bh) = 7.81(+/-0.08) +
2.69(+/-0.28)[log(n/3)] with epsilon_(intrin)=0.31 dex, we investigated the
possibility of a higher order M_bh-n relation, finding the second order term in
the best-fitting quadratic relation to be inconsistent with a value of zero at
greater than the 99.99% confidence level. The optimal relation is given by
log(M_bh) = 7.98(+/-0.09) + 3.70(+/-0.46)[log(n/3)] -
3.10(+/-0.84)[log(n/3)]^2, with epsilon_(intrin)=0.18 dex and a total absolute
scatter of 0.31 dex. Extrapolating the quadratic relation, it predicts black
holes with masses of ~10^3 M_sun in n=0.5 dwarf elliptical galaxies, compared
to ~10^5 M_sun from the linear relation, and an upper bound on the largest
black hole masses in the local universe, equal to 1.2^{+2.6}_{-0.4}x10^9
M_sun}. In addition, we show that the nuclear star clusters at the centers of
low-luminosity elliptical galaxies follow an extrapolation of the same
quadratic relation. Moreover, we speculate that the merger of two such
nucleated galaxies, accompanied by the merger and runaway collision of their
central star clusters, may result in the late-time formation of some
supermassive black holes. Finally, we predict the existence of, and provide
equations for, a relation between M_bh and the central surface brightness of
the host bulge.
