What if we take the birthday "paradox" into account ? Unfortunately Wolfram Alpha refuses to calculate the result for very big N. Also: I'm the only one seein

What if we take the birthday "paradox" into account ? Unfortunately Wolfram Alpha refuses to calculate the result for very big N. Also: I'm the only one seeing this Hacker News page because it says "kaoD" at the top-right, and I'm the only one who knows my password (or at least I hope so).