469. Empty chairs
http://projecteuler.net/problem=469
房間裡有個圓桌，周圍有 N 張椅子。
騎士們依序進來並隨機坐在其中一個椅子上。
為了使得手肘有伸展的空間，騎士們會在彼此之間留下至少一個空椅子。
當已經沒有任何人可以入座後，檢視此時空椅子佔的比例 C。
令 E(N) 表示 C 的期望值。
給定 E(4) = 1/2, E(6) = 5/9，求 E(10^18)。將答案四捨五入至小數第十四位。
--
'You've sort of made up for it tonight,' said Harry. 'Getting the
sword. Finishing the Horcrux. Saving my life.'
'That makes me sound a lot cooler then I was,' Ron mumbled.
'Stuff like that always sounds cooler then it really was,' said
Harry. 'I've been trying to tell you that for years.'
-- Harry Potter and the Deathly Hollows, P.308
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