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Search: id:A094033
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| A094033 |
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Number of connected 2-element antichains on a labeled n-set. |
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+0
16
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| 0, 0, 0, 3, 18, 75, 270, 903, 2898, 9075, 27990, 85503, 259578, 784875, 2366910, 7125303, 21425058, 64373475, 193317030, 580344303, 1741819338, 5227030875, 15684238350, 47059006503, 141189602418, 423593973075, 1270832250870
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Let P(A) be the power set of an n-element set A. Then a(n+1) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 1) x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008
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FORMULA
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E.g.f.: (exp(3*x)-3*exp(2*x)+3*exp(x)-1)/2!.
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MAPLE
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[seq (stirling2(n, 3)*3, n=0..26)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 06 2006
restart:with (combinat):a:=n->(sum((stirling2(n, 3)), j=3..n)):seq(a(n), n=0..40): b:=n->(sum((stirling2(n, 3)), j=0..n)):seq(b(n), n=0..40): c:=b-a:seq(c(n), n=0..26); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
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CROSSREFS
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Cf. A000392, A016269, A047707, A051112-A051118, A094033-A094037.
Adjacent sequences: A094030 A094031 A094032 this_sequence A094034 A094035 A094036
Sequence in context: A135070 A073961 A059393 this_sequence A043008 A056319 A056310
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KEYWORD
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nonn
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AUTHOR
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Goran Kilibarda, Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 22 2004
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