Coin probability problem

We throw the coin 1 000 000 times. How many times on average will make 13 successful heads? Now the problem with the naive:
1 000 000/(2^13) is that once it made 13 heads the 14 head will happen with 1/2 probability , but it will count as 2 13 successful heads. 15 will happen 4xtimes less, but it will count as 3 13 successful heads. (which is far more probable than 3x1 000 000/(2^13)) if they were happening discretely. Monte carlo simulation also suggests something is fishy:
So what exactly is the expected number of 13 successful heads?