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We present the blind Westerbork Coma Survey probing the H I content of the Coma galaxy cluster with the Westerbork Synthesis Radio Telescope. The survey covers the inner ∼1 Mpc around the cluster centre, extending out to 1.5 Mpc towards the south-western NGC 4839 group. The survey probes the atomic gas in the entire Coma volume down to a sensitivity of ∼1019 cm−2 and 108 M⊙. Combining automated source finding with source extraction at optical redshifts and visual verification, we obtained 40 H I detections of which 24 are new. Over half of the sample displays perturbed H I morphologies indicative of an ongoing interaction with the cluster environment. With the use of ancillary UV and mid-IR, data we measured their stellar masses and star formation rates and compared the H I properties to a set of field galaxies spanning a similar stellar mass and star formation rate range. We find that ∼75% of H I-selected Coma galaxies have simultaneously enhanced star formation rates (by ∼0.2 dex) and are H I deficient (by ∼0.5 dex) compared to field galaxies of the same stellar mass. According to our toy model, the simultaneous H I deficiency and enhanced star formation activity can be attributed to either H I stripping of already highly star forming galaxies on a very short timescale, while their H2 content remains largely unaffected, or to H I stripping coupled to a temporary boost of the H I-to-H2 conversion, causing a brief starburst phase triggered by ram pressure before eventually quenching the galaxy. © ESO 2022. ; This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 679627; project name FORNAX). JMvdH and KMH acknowledge funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 291531 ('HIStoryNU'). LC acknowledges support from the Australian Research Councils Discovery Project and Future Fellowship funding schemes (DP210100337,FT180100066). Parts of this research were conducted by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. JH acknowledges research funding from the South African Radio Astronomy Observatory. MV acknowledges support by the Netherlands Foundation for Scientific Research (NWO) through VICI grant 016.130.338. KMH acknowledges funding from the State Agency for Research of the Spanish Ministry of Science, Innovation and Universities through the "Center of Excellence Severo Ochoa" awarded to the Instituto de Astrofísica de Andalucía (SEV-2017-0709); from grant RTI2018-096228-B-C31 (Ministry of Science, Innovation and Universities / State Agency for Research / European Regional Development Funds, European Union); and from the coordination of the participation in SKA-SPAIN, funded by the Ministry of Science and innovation (MICIN). ; Peer reviewed