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Search: id:A004123
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| A004123 |
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Number of generalized weak orders on n points.
(Formerly M1975)
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+0
9
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| 1, 2, 10, 74, 730, 9002, 133210, 2299754, 45375130, 1007179562, 24840104410, 673895590634, 19944372341530, 639455369290922, 22079273878443610, 816812844197444714, 32232133532123179930, 1351401783010933015082
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of bipartitional relations on a set of cardinality n. - Ralf Stephan, Apr 27 2003
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REFERENCES
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Wagner, Carl G.; Enumeration of generalized weak orders. Arch. Math. (Basel) 39 (1982), no. 2, 147-152.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
P. Blasiak, K. A. Penson and A. I. Solomon, Dobinski-type relations and the log-normal distribution.
C. G. Bower, Transforms
Foata, D. and Krattenthaler, C., Graphical Major Indices, II, Seminaire Lotharingien de Combinatoire, B34k, 16 pp., 1995.
D. Foata and D. Zeilberger, [math/9406220] The Graphical Major Index
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FORMULA
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a(n) = sum(k^n*(2/3)^k, k = 0..infinity)/3; a(n) = sum(stirling2(n, k)*(2^k)*k!, k = 0..n); E.g.f. : 1/(3-2*exp(x))
Stirling transform of A000165. - Karol A. Penson (penson(AT)lptl.jussieu.fr), Jan 25 2002
"AIJ" (ordered, indistinct, labeled) transform of 2, 2, 2, 2...
Recurrence: a(n) = 2*Sum_{k=1..n} binomial(n, k)*a(n-k), a(0)=1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 27 2003
E.g.f.: 1/(3 - 2e^x).
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CROSSREFS
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Cf. A004121, A004122, A000165, A000670, A032033.
Second row of array A094416 (generalized ordered Bell numbers).
Equals 2 * A050351(n) for n>0.
Sequence in context: A046863 A000698 A092881 this_sequence A086352 A005365 A059104
Adjacent sequences: A004120 A004121 A004122 this_sequence A004124 A004125 A004126
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net)
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