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 A305935 Number of labeled spanning intersecting set-systems on n vertices with no singletons. 3
 1, 0, 1, 12, 809, 1146800, 899927167353, 291136684655893185321964, 14704020783497694096988185391720223222562121969, 12553242487939982849962414795232892198542733492886483991398790450208264017757788101836749760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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. A singleton is an edge containing only one vertex. LINKS Table of n, a(n) for n=0..9. FORMULA a(n) = A305843(n) - n * A003465(n-1). Inverse binomial transform of A306000. - Andrew Howroyd, Aug 12 2019 EXAMPLE The a(3) = 12 spanning intersecting set-systems with no singletons: {{1,2,3}} {{1,2},{1,3}} {{1,2},{2,3}} {{1,3},{2,3}} {{1,2},{1,2,3}} {{1,3},{1,2,3}} {{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}} {{1,2},{1,3},{2,3},{1,2,3}} CROSSREFS Cf. A001206, A006126, A051185, A048143, A058891, A305001, A305843, A305844, A305854-A305857, A305999, A306000, A306001, A306008. Sequence in context: A155813 A220119 A178023 * A228182 A356186 A003748 Adjacent sequences: A305932 A305933 A305934 * A305936 A305937 A305938 KEYWORD nonn AUTHOR Gus Wiseman, Jun 15 2018 EXTENSIONS a(6)-a(8) from Giovanni Resta, Jun 20 2018 a(9) from Andrew Howroyd, Aug 12 2019 STATUS approved

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Last modified December 10 22:19 EST 2023. Contains 367717 sequences. (Running on oeis4.)