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A266910
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Number of size 2 subsets of S_n that generate a transitive subgroup of S_n.
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1
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1, 12, 210, 5520, 206760, 10473120, 688821840, 57039171840, 5805880778880, 712594633766400, 103804864923513600, 17709509301413529600, 3498328696524626764800, 792308057159314683187200, 203965258080479292004608000, 59229266937652347633377280000, 19270409372174365076286590976000
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OFFSET
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2,2
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LINKS
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FORMULA
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EXAMPLE
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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)}.
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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