Context. The relationship between an active galactic nucleus (AGN) and its host galaxy is still far from being understood. Properties of the host galaxies of Seyfert nuclei, such as luminosity concentration, morphological type, metallicity, and age of the stellar population, are expected to be related with nuclear activity – either at the epoch of galaxy formation or at the present day via feeding of the central black hole. Aims. In this paper, we investigate whether stellar ages and metallicities are linked to the activity within the nucleus in a sample of AGNs of various types. Methods. Our sample includes seven AGNs, from Seyfert 1 to LINERs, observed with VLT/ISAAC and VLT/SINFONI. Based on an inverse method using a stellar library, we analysed H band infrared spectra, in a wavelength region devoid of emission lines, at a spectral resolution of ≈3000, in the few central 100 pc. Hubble Space Telescope images were used to visualise the regions defined in each galaxy. Results. For each galaxy, we give the results of the spectral synthesis, in particular the percentages of the stellar, power law, and black-body continua, and the percentages of various stellar types that account for the stellar lines. Conclusions. Out of the seven galaxies, three show strong and recent star formation in the inner 100 pc, while no star formation is detected in the three genuine Seyfert 2 galaxies. Beyond a radius of 100 pc, all show more or less recent star formation. Moreover, we can conclude that the star formation history of the inner nucleus is highly heterogeneous.