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 A268223 Triangle read by rows: T(n,k) (n>=6, k=3..n+1) is the number of topologies t on n points having exactly k open sets such that t contains exactly one open set of size m for each m in {0,5,6,7,...,s,n} where s is the size of the largest proper open set in t. 5
 6, 21, 42, 56, 168, 336, 126, 504, 1512, 3024, 252, 1260, 5040, 15120, 30240, 462, 2772, 13860, 55440, 166320, 332640, 792, 5544, 33264, 166320, 665280, 1995840, 3991680, 1287, 10296, 72072, 432432, 2162160, 8648640, 25945920, 51891840 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 6,1 LINKS Table of n, a(n) for n=6..41. G. A. Kamel, Partial Chain Topologies on Finite Sets, Computational and Applied Mathematics Journal. Vol. 1, No. 4, 2015, pp. 174-179. EXAMPLE Triangle begins: 6, 21,42, 56,168,336, 126,504,1512,3024, 252,1260,5040,15120,30240, ... MATHEMATICA i = 5; Table[ Table[Binomial[n, i] FactorialPower[n - i, k], {k, 0, n - i - 1}], {n, 2, 13}] // Grid (* Geoffrey Critzer, Feb 19 2017 *) CROSSREFS Row sums give A268219. Triangles in this series: A268216, A268217, A268221, A268222, A268223. Sequence in context: A225150 A056237 A199194 * A048036 A272671 A272684 Adjacent sequences: A268220 A268221 A268222 * A268224 A268225 A268226 KEYWORD nonn,tabl,more AUTHOR N. J. A. Sloane, Jan 30 2016 EXTENSIONS Title clarified and more terms added by Geoffrey Critzer, Feb 19 2017 STATUS approved

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Last modified May 29 11:32 EDT 2023. Contains 363042 sequences. (Running on oeis4.)