B737 pilot reported a NMAC with a helicopter after takeoff following a vector from ATC. Helicopter pilot descended to avoid colliding with the B737.

Narrative

We taxied out to Runway XXC at ZZZ. The airport was very busy. We were #6 in the pad waiting for departure. There were two Law Enforcement helicopters following a vehicle just west of the airport. A Company 737 in front of us was given a confusing clearance to avoid the helicopters on departure. We watched on TCAS as they just missed the helicopters. Before we departed; the 2 helicopters crossed the departure end of XXC and moved to the north of the airport. During this time ATC lost communications with one of the helicopters. The ZZZ Tower Controller seamed very busy. We were cleared for departure with a right turn to heading 110. While in the climbing right turn we realized we were very close to the helicopters. We did not know what direction they were going or if they were changing altitude. We followed our clearance and waited for a RA from our TCAS. We never saw the helicopter because I was concentrating inside on flying the aircraft trying to climb overtop of the helicopters. The Captain couldn't see them because we were in a nose up attitude. The one helicopter saw us and radioed they were descending to avoid us. According to TCAS we went right over top of them by 100 feet. Helicopters should not operate right off the end of a busy runway! ATC should not vector aircraft on a collision course.