A267575
Number of size 3 subsets of S_n that generate a transitive group.
Original entry on oeis.org
20, 1932, 269040, 60018480, 20842305120, 10739272592160, 7859814146553600, 7880871595516819200, 10509569407728543398400, 18186461035281996953126400, 39999355842324635340366182400, 109852416743246886658078908979200, 371006429409575280027759776435712000
Offset: 3
-
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]
A327547
Triangular array read by rows: T(n,k) is the number of ordered pairs of n-permutations that generate a group with exactly k orbits, 0 <= k <= n, n >= 0.
Original entry on oeis.org
1, 0, 1, 0, 3, 1, 0, 26, 9, 1, 0, 426, 131, 18, 1, 0, 11064, 2910, 395, 30, 1, 0, 413640, 92314, 11475, 925, 45, 1, 0, 20946960, 3980172, 438424, 34125, 1855, 63, 1, 0, 1377648720, 224782284, 21632436, 1550689, 84840, 3346, 84, 1, 0, 114078384000, 16158371184, 1353378284, 87036012, 4533249, 185976, 5586, 108, 1
Offset: 0
Triangle T(n,k) begins:
1;
0, 1;
0, 3, 1;
0, 26, 9, 1;
0, 426, 131, 18, 1;
0, 11064, 2910, 395, 30, 1;
0, 413640, 92314, 11475, 925, 45, 1;
T(3,2) = 9 because we have 3 ordered pairs (e,<(1,2)>), (<(1,2)>,e), (<(1,2)>,<(1,2)>) for each of the 3 transpositions in S_3.
-
nn = 7; Range[0, nn]! CoefficientList[Series[Exp[u Log[Sum[n!^2 z^n/n!, {n, 0, nn}]]], {z, 0, nn}], {z, u}] // Grid
Showing 1-2 of 2 results.