A267575 Number of size 3 subsets of S_n that generate a transitive group.
20, 1932, 269040, 60018480, 20842305120, 10739272592160, 7859814146553600, 7880871595516819200, 10509569407728543398400, 18186461035281996953126400, 39999355842324635340366182400, 109852416743246886658078908979200, 371006429409575280027759776435712000
Offset: 3
Keywords
Programs
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Mathematica
nn = 15; b = Sum[n!^3 x^n/n!, {n, 0, nn}]; a = Sum[n!^2 x^n/n!, {n, 0, 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]