On the Hoge Veluwe National Park in September is the rutting season of the Red Deer. I visited the area and was lucky to see two males one of which obliged with making the sounds and right movements. The ranger threw apples around which attracted them.
First the females appeared
The male soon followed
The antler is magnificent !
Go to https://www.youtube.com/watch?v=DmKo5-VbmSM to hear the sound
I wasn't the only one there