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A268221
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Triangle read by rows: T(n,k) (n>=4, 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 {0,3,4,5,...,s,n} where s is the size of the largest proper open set in t.
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5
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4, 10, 20, 20, 60, 120, 35, 140, 420, 840, 56, 280, 1120, 3360, 6720, 84, 504, 2520, 10080, 30240, 60480, 120, 840, 5040, 25200, 100800, 302400, 604800, 165, 1320, 9240, 55440, 277200, 1108800, 3326400, 6652800, 220, 1980, 15840, 110880, 665280, 3326400, 13305600, 39916800, 79833600
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OFFSET
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4,1
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LINKS
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EXAMPLE
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Triangle begins:
4,
10,20,
20,60,120,
35,140,420,840,
56,280,1120,3360,6720,
84,504,2520,10080,30240,60480,
120,840,5040,25200,100800,302400,604800,
...
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MATHEMATICA
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i = 3; Table[Table[Binomial[n, i] FactorialPower[n - i, k], {k, 0, n - i - 1}], {n, 2, 12}] // Grid (* Geoffrey Critzer, Feb 19 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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