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 A282507 Triangular array read by rows. T(n,k) is the number of chain topologies on an n-set with exactly k open sets where one of the open sets is a single point set, n>=2, 3<=k<=n+1. 4
 2, 3, 6, 4, 24, 24, 5, 70, 180, 120, 6, 180, 900, 1440, 720, 7, 434, 3780, 10920, 12600, 5040, 8, 1008, 14448, 67200, 134400, 120960, 40320, 9, 2286, 52164, 367416, 1134000, 1723680, 1270080, 362880, 10, 5100, 181500, 1864800, 8341200, 19051200, 23284800, 14515200, 3628800 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS A chain topology is a topology that can be totally ordered by inclusion. LINKS FORMULA E.g.f.: y^2*x/(1 - y*(exp(x) - 1)). Generally for chain topologies where the smallest nonempty open set has size m: x^m/m! * y^2/(1 - y*(exp(x) - 1)). EXAMPLE 2   3   6   4   24   24   5   70   180   120   6   180  900   1440   720 MATHEMATICA nn = 10; Map[Select[#, # > 0 &] &, Drop[Range[0, nn]! CoefficientList[Series[   x/(1 - y (Exp[x] - 1)), {x, 0, nn}], {x, y}], 2]] // Grid CROSSREFS Cf. A268216 where the topologies are further restricted. Row sums = A052882. Sequence in context: A248090 A229774 A137524 * A156055 A096357 A091507 Adjacent sequences:  A282504 A282505 A282506 * A282508 A282509 A282510 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Feb 16 2017 STATUS approved

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Last modified January 21 20:04 EST 2019. Contains 319350 sequences. (Running on oeis4.)