login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; table; graph; refs; listen; history; text; internal format)
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. 174-179.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 15 23:40 EDT 2021. Contains 343007 sequences. (Running on oeis4.)