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%I #21 Apr 29 2023 14:09:14
%S 128,128,128,128,128,128,128,128,128,128,128,128,32768,32768,2097152,
%T 8388608,8388608,16777216,4194304,8388608,4194304,16777216,8388608,
%U 16777216,16777216,16777216,4194304,2097152,4194304,4194304,16777216,16777216,16777216
%N Number of possible ways to fill out NCAA Division I Men's Basketball Tournament Office Pool by year, 1939-2011.
%C The number a(n) is 2^(k-1) where k is the number of teams in the tournament in year n. The sequence includes any play-in games in preliminary rounds but does not include regional or national third place games.
%C The number of teams year by year is as follows (source: Wikipedia, detailed list in the b-file):
%C 1939-1950: eight teams; 1951-1952: 16 teams; 1953-1974: varied between 22 and 25 teams; 1975-1978: 32 teams; 1979: 40 teams; 1980-1982: 48 teams; 1983: 52 teams (four play-in games before the tournament); 1984: 53 teams (five play-in games before the tournament); 1985-2000: 64 teams; 2001-2010: 65 teams (with an opening round game to determine whether the 64th or 65th team plays in the first round); 2011-future: 68 teams (four play-in games before the tournament, the nominal first round).
%C An office pool is where people try to predict the outcome of every single NCAA Tournament game before it starts. The probability of doing so perfectly by randomly choosing is 1/a(n).
%H Georg Fischer, <a href="/A187353/b187353.txt">Table of n, a(n) for n = 1939..2011</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/NCAA_Men%27s_Division_I_Basketball_Tournament">NCAA Men's Division I Basketball Championship</a> for the number of teams year-by-year, as well as the articles on individual tournaments between 1953-1974 as those do not have specific numbers listed on the main page.
%F a(n) = 2^(k-1) where k = number of teams in the NCAA Tournament of year n.
%e a(1939) = 2^(8-1) = 2^7 = 128 since there were 8 teams in the 1939 NCAA Tournament.
%K dumb,easy,fini,full,nonn
%O 1939,1
%A _Gregory Koch_, Mar 08 2011
%E Edited by _Georg Fischer_, Mar 19 2019