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A268221 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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

4,1

LINKS

Table of n, a(n) for n=4..48.

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:

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,

...

MATHEMATICA

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 *)

CROSSREFS

Row sums give A268218.

Triangles in this series: A268216, A268217, A268221, A268222, A268223.

Cf. A282507.

Sequence in context: A155229 A155220 A300018 * A086176 A015789 A145021

Adjacent sequences:  A268218 A268219 A268220 * A268222 A268223 A268224

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 12 01:50 EDT 2021. Contains 343808 sequences. (Running on oeis4.)