The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326961 Number of set-systems covering n vertices where every vertex is the unique common element of some subset of the edges, also called covering T_1 set-systems. 17
 1, 1, 2, 36, 19020, 2010231696, 9219217412568364176, 170141181796805105960861096082778425120, 57896044618658097536026644159052312977171804852352892309392604715987334365792 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Same as A059523 except with a(1) = 1 instead of 2. Alternatively, these are set-systems covering n vertices whose dual is a (strict) antichain. A set-system is a finite set of finite nonempty sets. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. An antichain is a set of sets, none of which is a subset of any other. LINKS Table of n, a(n) for n=0..8. FORMULA Inverse binomial transform of A326965. EXAMPLE The a(3) = 36 set-systems: {{1}{2}{3}} {{12}{13}{23}{123}} {{2}{3}{12}{13}{23}} {{12}{13}{23}} {{1}{2}{3}{12}{13}} {{2}{3}{12}{13}{123}} {{1}{2}{3}{12}} {{1}{2}{3}{12}{23}} {{2}{12}{13}{23}{123}} {{1}{2}{3}{13}} {{1}{2}{3}{13}{23}} {{3}{12}{13}{23}{123}} {{1}{2}{3}{23}} {{1}{2}{12}{13}{23}} {{1}{2}{3}{12}{13}{23}} {{1}{2}{13}{23}} {{1}{2}{3}{12}{123}} {{1}{2}{3}{12}{13}{123}} {{1}{2}{3}{123}} {{1}{2}{3}{13}{123}} {{1}{2}{3}{12}{23}{123}} {{1}{3}{12}{23}} {{1}{2}{3}{23}{123}} {{1}{2}{3}{13}{23}{123}} {{2}{3}{12}{13}} {{1}{3}{12}{13}{23}} {{1}{2}{12}{13}{23}{123}} {{1}{12}{13}{23}} {{1}{2}{13}{23}{123}} {{1}{3}{12}{13}{23}{123}} {{2}{12}{13}{23}} {{1}{3}{12}{23}{123}} {{2}{3}{12}{13}{23}{123}} {{3}{12}{13}{23}} {{1}{12}{13}{23}{123}} {{1}{2}{3}{12}{13}{23}{123}} MATHEMATICA tmQ[eds_]:=Union@@Select[Intersection@@@Rest[Subsets[eds]], Length[#]==1&]==Union@@eds; Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Union@@#==Range[n]&&tmQ[#]&]], {n, 0, 3}] CROSSREFS Covering set-systems are A003465. Covering T_0 set-systems are A059201. The version with empty edges allowed is A326960. The non-covering version is A326965. Covering set-systems whose dual is a weak antichain are A326970. The unlabeled version is A326974. The BII-numbers of T_1 set-systems are A326979. Cf. A058891, A059052, A059523, A323818, A326972, A326973, A326976, A326977. Sequence in context: A134366 A265944 A127234 * A181555 A306644 A283261 Adjacent sequences: A326958 A326959 A326960 * A326962 A326963 A326964 KEYWORD nonn AUTHOR Gus Wiseman, Aug 12 2019 STATUS approved

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

Last modified September 29 02:45 EDT 2023. Contains 365749 sequences. (Running on oeis4.)