Thank you 
Indeed scaling by (window size - 1) / (window size) shows this is so.
As for the correctness of using the Bessel correction on an activation map where the values are definitely not independent, that’s another story. I guess the “correct scaling” lies somewhere in
(batch size - 1) / (batch size)  < “correct scaling” < ( batch size * window size - 1 ) * (batch size * window size ).
Anyway, question answered