Interesting idea, but I don't quite get how that lets us compute the answer. If I understand it correctly then we need to get the coefficient of l^(10^6) of (e^

Interesting idea, but I don't quite get how that lets us compute the answer. If I understand it correctly then we need to get the coefficient of l^(10^6) of (e^-(l/20000) + (l/20000)e^-(l/20000) + (l/20000)^2/2e^-(l/20000))^20000, and I do not know how to do that. In fact that is equivalent to finding the coefficient of x^(10^6) of (1+x+x^2)^20000, and it's easy too see that directly from the original problem, so I'm also not sure what Poissonization does for us here. Perhaps I'm completely misunderstanding the technique?