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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 (list; table; graph; refs; listen; history; text; internal format)
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. 174-179.

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

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Last modified May 11 18:21 EDT 2021. Contains 343808 sequences. (Running on oeis4.)