A266910 Number of size 2 subsets of S_n that generate a transitive subgroup of S_n.

1, 12, 210, 5520, 206760, 10473120, 688821840, 57039171840, 5805880778880, 712594633766400, 103804864923513600, 17709509301413529600, 3498328696524626764800, 792308057159314683187200, 203965258080479292004608000, 59229266937652347633377280000, 19270409372174365076286590976000

Offset: 2

Author

Geoffrey Critzer, Jan 05 2016

Keywords

• nonn

Examples

			a(3) = 12 because there are 15 = binomial(3!,2)  size 2 subsets of S_3 and every such subset generates a transitive subgroup of S_3 except: {(),(12)}, {(),(13)}, {(),(23)}.
		

Crossrefs

Cf. A122949.

Programs

Mathematica

nn = 20; a = Sum[n!^2 x^n/n!, {n, 0, nn}]; Drop[(Range[0, nn]! CoefficientList[Series[Log[a], {x, 0, nn}], x] - Table[(n - 1)!, {n, 0, nn}])/2, 2]

Formula

a(n) = (A122949(n) - (n - 1)!)/2.