Fifteen Consecutive "9"s

I read a book today, and I found one interesting problem.

There are a lot of integers which consist of one "1", two "2"s, three "3"s, ... , eight "8"s and nine "9"s. If you sum all these 45-digit integers up, there are fifteen consecutive "9"s in the answer.

There is no coincidence. Can you explain why?

(Hint: To explain this phenomenon, you need only shallow knowledge in combinatorics and number theory.)