Rapid formation of a very massive star (>50000 M

Context. We present simulations of a massive young star cluster using the codes N<ns0:sc>body</ns0:sc>6++GPU and MOCCA. The cluster is initially more compact than previously published models. It contains one million stars and has a total mass of 5.86 × 105 M⊙ and a half-mass radius of 0.1 pc. Aims. We analyzed the formation and growth of a very massive star (VMS) through successive stellar collisions and investigated the subsequent formation of an intermediate-mass black hole (IMBH) in the core of a dense star cluster. Methods. We used direct N-body and Monte Carlo simulations that incorporated updated stellar evolution prescriptions for single and binary stellar evolution (SSE and BSE) tailored to massive stars and VMSs. These include revised treatments of stellar radii, rejuvenation, and mass loss during collisions. While the prescriptions represent reasonable extrapolations into the VMS regime, the internal structure and thermal state of VMSs that formed through stellar collisions remain uncertain, and future work may require further refinement. Results. Runaway stellar collisions in the cluster core produce a VMS that exceeds 5 × 104 M⊙ within 5 Myr that subsequently collapses into an IMBH. We stress that further work on stellar astrophysics is needed, particularly in the context of VMS formation. The VMS formation currently represents strong uncertainties. Conclusions. Our model suggests that dense stellar environments may enable the formation of VMSs and massive black hole seeds through runaway stellar collisions. These results provide a potential pathway for early black hole growth in star clusters and offer a theoretical context for interpreting recent observations with the James Webb Space Telescope of young compact clusters at high redshift.