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 A137736 Number of set partitions of n(n-1)/2. 1
 0, 1, 5, 203, 115975, 1382958545, 474869816156751, 6160539404599934652455, 3819714729894818339975525681317, 139258505266263669602347053993654079693415 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Among n persons we have (n^2-n)/2 undirected relations. We can set partition these relations into (up to) A137736(n)=Bell((n^2-n)/2) sets. The number of graphs on n labeled nodes is A006125(n)=sum(binomial((n^2-n)/2,k),k=0..(n^2-n)/2). The number of set partitions of n(n-1)/2 is A137736(n)=sum(Stirling2((n^2-n)/2,k),k=0..(n^2-n)/2). See also A066655 which equals A066555(n)=sum(P((n^2-n)/2,k),k=0..(n^2-n)/2) where P(n) is the number of integer partitions of n. See also A135084 = A000110(2^n-1) and A135085 = A000110(2^n). LINKS FORMULA a(n) = Bell(n(n-1)/2) = A000110(n(n-1)/2) EXAMPLE a(4) = Bell(6) = 203. MAPLE for n from 1 to 10 do a(n):=bell((n^2-n)/2): print(a(n)); od: CROSSREFS Cf. A006125, A066655, A135084, A135085. Sequence in context: A208468 A070906 A208052 * A157389 A128678 A232987 Adjacent sequences:  A137733 A137734 A137735 * A137737 A137738 A137739 KEYWORD nonn AUTHOR Thomas Wieder, Feb 09 2008 STATUS approved

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Last modified July 30 04:51 EDT 2021. Contains 346348 sequences. (Running on oeis4.)