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 A305843 Number of labeled spanning intersecting set-systems on n vertices. 41
 1, 1, 3, 27, 1245, 1308285, 912811093455, 291201248260060977862887, 14704022144627161780742038728709819246535634969, 12553242487940503914363982718112298267975272588471811456164576678961759219689708372356843289 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge. LINKS FORMULA Inverse binomial transform of A051185. EXAMPLE The a(3) = 27 spanning intersecting set-systems: {{1,2,3}} {{1},{1,2,3}} {{2},{1,2,3}} {{3},{1,2,3}} {{1,2},{1,3}} {{1,2},{2,3}} {{1,2},{1,2,3}} {{1,3},{2,3}} {{1,3},{1,2,3}} {{2,3},{1,2,3}} {{1},{1,2},{1,3}} {{1},{1,2},{1,2,3}} {{1},{1,3},{1,2,3}} {{2},{1,2},{2,3}} {{2},{1,2},{1,2,3}} {{2},{2,3},{1,2,3}} {{3},{1,3},{2,3}} {{3},{1,3},{1,2,3}} {{3},{2,3},{1,2,3}} {{1,2},{1,3},{2,3}} {{1,2},{1,3},{1,2,3}} {{1,2},{2,3},{1,2,3}} {{1,3},{2,3},{1,2,3}} {{1},{1,2},{1,3},{1,2,3}} {{2},{1,2},{2,3},{1,2,3}} {{3},{1,3},{2,3},{1,2,3}} {{1,2},{1,3},{2,3},{1,2,3}} MATHEMATICA Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]], And[Union@@#==Range[n], FreeQ[Intersection@@@Tuples[#, 2], {}]]&], {n, 1, 4}] CROSSREFS Cf. A001206, A006126, A048143, A051185, A134958, A030019, A304985, A305844. Sequence in context: A279832 A012012 A229866 * A192341 A191511 A102580 Adjacent sequences:  A305840 A305841 A305842 * A305844 A305845 A305846 KEYWORD nonn AUTHOR Gus Wiseman, Jun 11 2018 STATUS approved

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Last modified September 23 16:48 EDT 2021. Contains 347618 sequences. (Running on oeis4.)