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%I #23 Oct 13 2022 12:45:56
%S 240,2880,33600,403200,5093760,68275200,972787200,14724864000,
%T 236396160000,4016659046400,72067387392000,1362306097152000,
%U 27071765360640000,564357385912320000,12317692759916544000,280955128203509760000
%N Number of n-node tournaments that have exactly three circular triads.
%H J. B. Kadane, <a href="https://doi.org/10.1214/aoms/1177699532">Some equivalence classes in paired comparisons</a>, The Annals of Mathematical Statistics, 37 (1966), 488-494.
%F a(n) = n!*(2*(n-4) + (1/3)*(n-5)*(n-6) + (1/162)*(n-6)*(n-7)*(n-8)*[n>5]) (see Kadane).
%F E.g.f.: (x^4 - 18*x^3 + 72*x^2 - 108*x + 54)*x^5/((3^3)*(1-x)^4).
%e a(6) = 6!*(2*(6-4) + (1/3)*(6-5)*(6-6) + (1/162)*(6-6)*(6-7)*(6-8)*[6>5]) = 2880.
%t Table[n!*(2*(n-4) + (1/3)*(n-5)*(n-6) + (1/162)*(n-6)*(n-7)*(n-8)*Boole[n>5]), {n,5,20}] (* _Stefano Spezia_, Sep 27 2022 *)
%Y Cf. A357242, A357248, A357266.
%K nonn
%O 5,1
%A _Ian R Harris_, _Ryan P. A. McShane_, Sep 20 2022