

A059201


Number of T_0covers of a labeled nset.


64



1, 1, 4, 96, 31692, 2147001636, 9223371991763269704, 170141183460469231473432887375376674952, 57896044618658097711785492504343953920509909728243389682424010192567186540224
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OFFSET

0,3


COMMENTS

A cover of a set is a T_0cover if for every two distinct points of the set there exists a member (block) of the cover containing one but not the other point.
From Gus Wiseman, Aug 13 2019: (Start)
A setsystem is a finite set of finite nonempty sets. The dual of a setsystem has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges). For example, the a(2) = 4 covers are:
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
{{1},{2},{1,2}}
(End)


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..11
Vladeta Jovovic, T_0covers of a labeled 3set


FORMULA

a(n) = Sum_{i=0..n+1} stirling1(n+1, i)*2^(2^(i1)1).
a(n) = Sum_{m=0..2^n1} A059202(n,m).
Inverse binomial transform of A326940 and exponential transform of A326948.  Gus Wiseman, Aug 13 2019


MATHEMATICA

Table[Sum[StirlingS1[n + 1, k]*2^(2^(k  1)  1), {k, 0, n + 1}], {n, 0, 5}] (* G. C. Greubel, Dec 28 2016 *)
dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}];
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Union@@#==Range[n]&&UnsameQ@@dual[#]&]], {n, 0, 3}] (* Gus Wiseman, Aug 13 2019 *)


CROSSREFS

Row sums of A059202.
Cf. A059203, A059084, A059085, A059086, A059087, A059088, A059089.
Covering setsystems are A003465.
The unlabeled version is A319637.
The version with empty edges allowed is A326939.
The noncovering version is A326940.
BIInumbers of T_0 setsystems are A326947.
The same with connected instead of covering is A326948.
The T_1 version is A326961.
Cf. A245567, A316978, A319559, A319564, A323818, A326941, A326946, A326970.
Sequence in context: A181335 A098695 A307934 * A323818 A027638 A309483
Adjacent sequences: A059198 A059199 A059200 * A059202 A059203 A059204


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic, Goran Kilibarda, Jan 16 2001


STATUS

approved



