  Gaussian boson sampling constitutes a prime candidate for an experimental
demonstration of quantum advantage within reach with current technological
capabilities. The original proposal employs photon-number-resolving detectors,
however the latter are not widely available. On the other hand, inexpensive
threshold detectors can be combined into a single click-counting detector to
achieve approximate photon number resolution. We investigate the problem of
sampling from a general multi-mode Gaussian state using click-counting
detectors and show that the probability of obtaining a given outcome is related
to a new matrix function which is dubbed as the Kensingtonian. We show how the
latter relates to the Torontonian and the Hafnian, thus bridging the gap
between known Gaussian boson sampling variants. We then prove that, under
standard complexity-theoretical conjectures, the model can not be simulated
efficiently.
