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Table[ n^2 - 2*n, {n, 0, 60} ] (* _George E. Antoniou _ *)
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(PARI) concat(0, Vec(x*(3*x-1)/(1-x)^3 + O(x^100))) \\ Altug Alkan, Oct 30 2015
(PARI) concat(0, Vec(x*(3*x-1)/(1-x)^3 + O(x^100))) \\ Altug Alkan, Oct 30 2015
Wikipedia, <a href="http://www.wikipedia.org/wiki/Monty_Hall_problem">Monty Hall problem</a>.
From Amiram Eldar, Feb 17 2023: (Start)
Sum_{n>=3} 1/a(n) = 3/4.
Sum_{n>=3} (-1)^(n+1)/a(n) = 1/4. (End)
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(MAGMAMagma) [n^2-2*n : n in [0..50]]; // Wesley Ivan Hurt, Sep 04 2014
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