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We report the detection of 18 Jovian planets discovered as part of our Doppler survey of subgiant stars at Keck Observatory, with follow-up Doppler and photometric observations made at McDonald and Fairborn Observatories, respectively. The host stars have masses 0.927 ⩽ M⋆/M☉ ⩽ 1.95, radii 2.5 ⩽ R⋆/R☉ ⩽ 8.7, and metallicities −0.46 ⩽ [Fe/H] ⩽+0.30. The planets have minimum masses 0.9 MJup ⩽ MPsin i ≲ 13 MJup and semimajor axes a ⩾ 0.76 AU. These detections represent a 50% increase in the number of planets known to orbit stars more massive than 1.5 M☉ and provide valuable additional information about the properties of planets around stars more massive than the Sun.