  We study the imprints on the formation of cosmic structures of a particular
class of dark energy parameterizations dubbed PADE parameterization. Here we
investigate how dark energy can affect the growth of large scale structures of
the universe in framework of spherical collapse model. The dynamics of the
spherical collapse of a dark matter halo depends on the properties of the dark
energy model. We show that the properties of spherical collapse scenario are
directly affected by the evolution of dark energy. We obtain the main
parameters of spherical collapse for two different DE parameterizations in two
different approaches: first the homogeneous DE approach, in which dark energy
does not exhibit fluctuations on cluster scales and the other, clustered DE
scenario in which, dark energy components inside the overdense region collapses
similar to dark matter. Using the Sheth-Tormen mass function, we investigate
the abundance of virialized halos in the framework of PADE parameterizations.
Specifically, the present analysis shows that the number count of dark matter
halos depends on the evolution of DE parameterizations and clustering
properties of dark energy. Also we show that perturbations in phantom DE
components enhance the growth of matter perturbations. This result were
obtained in the literature for dark energy parameterizations that are phantom
at all redshifts. But we obtained same results for dark energy
parameterizations which are in phantom regime and enter in quintessence region
at relatively low redshifts. We also show that in parameterizations under
study, low mass halos were formed before massive halos.
