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%I #18 May 05 2023 09:18:18
%S 1,6,720,31449600,444733651353600,10070314878246926155776000,
%T 614972203951464612786852376432607232000
%N Number of (2n+1) X (2n+1) symmetric matrices each of whose rows is a permutation of 1..(2n+1).
%C Number of different schedules for 2n+2 teams. - Andres Cardemil (andrescarde(AT)yahoo.com), Nov 28, 2001
%H Minjia Shi, Li Xu, Denis S. Krotov, <a href="https://arxiv.org/abs/1806.00009">The number of the non-full-rank Steiner triple systems</a>, arXiv:1806.00009 [math.CO], 2018.
%H <a href="/index/To#tournament">Index entries for sequences related to tournaments</a>
%F a(n) = A000438(n+1) * (2*n+1)!.
%Y Cf. A000438, A000474, A035481, A036980, A064120, A065594.
%K nonn,more
%O 0,2
%A _Joshua Zucker_ and Joe Keane
%E Two more terms computed from A000438 by _Max Alekseyev_, Jun 17 2011
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