The central kiloparsec region of the Andromeda galaxy is relatively gas poor, while the interstellar medium appears to be concentrated in a ring-like structure at about 10 kpc radius. The central gas depletion has been attributed to a possible head-on collision 200 Myr ago, supported by the existence of an offset inner ring of warm dust. We present new IRAM 30 m radio telescope observations of the molecular gas in the central region, and the detection of CO and its isotopes 13 CO(2−1) and C 18 O(2−1), together with the dense gas tracers, HCN(1−0) and HCO+(1−0). A systematic study of the observed peak temperatures with non-local thermal equilibrium simulations shows that the detected lines trace dense regions with n H 2 in the range 2.5 × 10 4 −5.6 × 10 5 cm −3 , while the gas is very clumpy with a beam filling factor of 0.5−2 × 10 −2 . This is compatible with the dust mass derived from the far-infrared emission, assuming a dust-to-gas mass ratio of 0.01 with a typical clump size of 2 pc. We also show that the gas is optically thin in all lines except for 12 CO(1-0) and 12 CO(2-1), CO lines are close to their thermal equilibrium condition at 17-20 K, the molecular hydrogen density is larger than critical, and HCN and HCO+ lines have a subthermal excitation temperature of 9 K with a density smaller than critical. The average 12 CO/ 13 CO line ratio is high (∼21), and close to the 12 CO/C 18 O ratio (∼30) that was measured in the north-western region and estimated in the south-east stacking. The fact that the optically thin 13 CO and C 18 O lines have comparable intensities means that the secondary element 13 C is depleted with respect to the primary 12 C, as is expected just after a recent star formation. This suggests that there has been a recent starburst in the central region, supporting the head-on collision scenario.