

A268222


Triangle read by rows: T(n,k) (n>=5, 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 {0,4,5,6,...,s,n} where s is the size of the largest proper open set in t.


5



5, 15, 30, 35, 105, 210, 70, 280, 840, 1680, 126, 630, 2520, 7560, 210, 1260, 6300, 25200, 75600, 151200, 330, 2310, 13860, 69300, 277200, 831600, 1663200, 495, 3960, 27720, 166320, 831600, 3326400, 9979200, 19958400
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OFFSET

5,1


LINKS

Table of n, a(n) for n=5..39.
G. A. Kamel, Partial Chain Topologies on Finite Sets, Computational and Applied Mathematics Journal. Vol. 1, No. 4, 2015, pp. 174179.


EXAMPLE

Triangle begins:
5,
15,30,
35,105,210,
70,280,840,1680,
126,630,2520,7560,15120,
210,1260,6300,25200,75600,151200,
...


MATHEMATICA

i = 4; 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 A268219.
Triangles in this series: A268216, A268217, A268221, A268222, A268223.
Cf. A282507.
Sequence in context: A162525 A212871 A188350 * A285630 A078905 A059160
Adjacent sequences: A268219 A268220 A268221 * A268223 A268224 A268225


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



