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abstract: 'The observed sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The standard Kingman coalescent model on genealogies – timed trees that represent the ancestry of the sample – is used in a generative model of molecular sequence variation to infer evolutionary parameters. However, the state space of Kingman’s genealogies grows superexponentially with sample size $n$, making inference computationally unfeasible already for small $n$. We introduce a new coalescent model called Tajima heterochronous n-coalescent with a substantially smaller cardinality of the genealogical space. This process allows to analyze samples collected at different times, a situation that in applications is both met (*e.g.* ancient DNA and RNA from rapidly evolving pathogens like viruses) and statistically desirable (variance reduction and parameter identifiability). We propose an algorithm to calculate the likelihood efficiently and present a Bayesian nonparametric procedure to infer the population size trajectory. We provide a new MCMC sampler to explore the space of Tajima’s genealogies and model parameters. We compare our procedure with state-of-the-art methodologies in simulations and applications. We use our method to re-examine the scientific question of how Beringian bison went extinct analyzing modern and ancient molecular sequences 