  We present the first systematic study of the molecular gas and star formation
efficiency in a sample of ten narrow-line Seyfert 1 galaxies selected to have
X-ray Ultra Fast Outflows and, therefore, to potentially show AGN feedback
effects. CO observations were obtained with the IRAM 30m telescope in six
galaxies and from the literature for four galaxies. We derived the stellar
mass, star formation rate, AGN and FIR dust luminosities by fitting the
multi-band spectral energy distributions with the CIGALE code. Most of the
galaxies in our sample lie above the main sequence (MS) and the molecular
depletion time is one to two orders of magnitude shorter than the one typically
measured in local star-forming galaxies. Moreover, we found a promising
correlation between the star formation efficiency and the Eddington ratio, as
well as a tentative correlation with the AGN luminosity. The role played by the
AGN activity in the regulation of star formation within the host galaxies of
our sample remains uncertain (little or no effect? positive feedback?).
Nevertheless, we can conclude that quenching by the AGN activity is minor and
that star formation will likely stop in a short time due to gas exhaustion by
the current starburst episode.
