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%I #15 Nov 14 2023 09:22:17
%S 1,2,12,104,1560,53184,3422384,430790144,111823251840,56741417927680,
%T 57729973360342272,118195918779085344768,479770203506298422135808,
%U 3914602958361039682677710848,63809077054456699374663196416000,2076906726499655025703507210668998656
%N Total number of highest scorers in all 2^(n(n-1)/2) tournaments with n players.
%C All highest scorers are also king chickens, A123553.
%H Andrew Howroyd, <a href="/A125031/b125031.txt">Table of n, a(n) for n = 1..20</a>
%H <a href="/index/To#tournament">Index entries for sequences related to tournaments</a>
%e With 4 players there are 32 tournaments with 1 highest scorer, 24 tournaments with 2 highest scorers and 8 tournaments with 3 highest scorers. Therefore a(4)=32*1+24*2+8*3=104.
%o (PARI) \\ Requires Winners from A013976.
%o a(n)={my(M=Winners(n)); sum(i=1, matsize(M)[1], pollead(M[i, 1])*M[i, 2])} \\ _Andrew Howroyd_, Feb 29 2020
%Y Cf. A006125, A013976, A123553, A125032, A123903.
%K nonn
%O 1,2
%A _Martin Fuller_, Nov 16 2006
%E a(5)-a(10) also computed by _Gordon Royle_, Nov 16 2006
%E Terms a(12) and beyond from _Andrew Howroyd_, Feb 28 2020
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