4s4p Li-Ion battery pack charging
A 16V power supply will be insufficient for your build. You need at least 17V supplied under load.

You could use a notebook charger rated at 19.5V. The protection circuit will handle the limitations, but you have to make sure that the charger can supply sufficient current for the whole pack. At 4 parallel cells, you'd need at least 4A supplied current (and use a charging at 1C).

Other than that, para-series charge is not generally recommended because a single bad cell over time will discharge the pair, which will not fully charge, which will end up with a bad pack consisting of 1 bad pair, 2 relatively good ones and 1 very good one.