

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
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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. 174179.


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



