  Young dense massive star clusters are a promising environment for the
formation of intermediate mass black holes (IMBHs) through collisions. We
present a set of 80 simulations carried out with Nbody6++GPU of 10 initial
conditions for compact $\sim 7 \times 10^4 M_{\odot}$ star clusters with
half-mass radii $R_\mathrm{h} \lesssim 1 pc$, central densities
$\rho_\mathrm{core} \gtrsim 10^5 M_\odot pc^{-3}$, and resolved stellar
populations with 10\% primordial binaries. Very massive stars (VMSs) with
masses up to $\sim 400 M_\odot$ grow rapidly by binary exchange and three-body
scattering events with main sequences stars in hard binaries. Assuming that in
VMS - stellar BH collisions all stellar material is accreted onto the BH, IMBHs
with masses up to $M_\mathrm{BH} \sim 350 M_\odot$ can form on timescales of
$\lesssim 15$ Myr. This process was qualitatively predicted from Monte Carlo
MOCCA simulations. Despite the stochastic nature of the process - typically not
more than 3/8 cluster realisations show IMBH formation - we find indications
for higher formation efficiencies in more compact clusters. Assuming a lower
accretion fraction of 0.5 for VMS - BH collisions, IMBHs can also form. The
process might not work for accretion fractions as low as 0.1. After formation,
the IMBHs can experience occasional mergers with stellar mass BHs in
intermediate mass-ratio inspiral events (IMRIs) on a 100 Myr timescale.
Realised with more than $10^5$ stars, 10 \% binaries, the assumed stellar
evolution model with all relevant evolution processes included and 300 Myr
simulation time, our large suite of simulations indicates that IMBHs of several
hundred solar masses might form rapidly in massive star clusters right after
their birth while they are still compact.
