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%I #8 Jan 17 2016 13:55:44
%S 20,1932,269040,60018480,20842305120,10739272592160,7859814146553600,
%T 7880871595516819200,10509569407728543398400,
%U 18186461035281996953126400,39999355842324635340366182400,109852416743246886658078908979200,371006429409575280027759776435712000
%N Number of size 3 subsets of S_n that generate a transitive group.
%F a(n) = (A220754(n) - 6*A266910 - (n-1)!)/6.
%t nn = 15; b = Sum[n!^3 x^n/n!, {n, 0, nn}]; a = Sum[n!^2 x^n/n!, {n, 0,
%t nn}]; c = (Range[0, nn]! CoefficientList[Series[Log[a], {x, 0, nn}], x] - Table[(n - 1)!, {n, 0, nn}])/ 2; Drop[((Range[0,nn]!CoefficientList[Series[Log[b], {x, 0, nn}], x]) - 6 c - Table[(n - 1)!, {n, 0, nn}])/6, 3]
%K nonn
%O 3,1
%A _Geoffrey Critzer_, Jan 17 2016
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