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Search: id:A132053
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| 1, 108, 7470, 429660, 22629915, 1143782640, 56936699820, 2835191759400, 142610008065525, 7291723635296100, 380553986882119050, 20327650785482940900, 1113292728197378103375, 62584367768103890709000
(list; graph; listen)
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OFFSET
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8,2
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COMMENT
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a(n), n>=8, enumerates unordered forests composed of eight plane increasing ternary trees with n vertices. See A001147 (number of increasing ternary trees) and a D. Callan comment there. For a picture of some ternary trees see a W. Lang link under A001764.
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FORMULA
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E.g.f. ((x*c(x/2)*(1-2*x)^(-1/2))^8)/8!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
E.g.f. (-1+(1-2*x)^(-1/2))^8/8!.
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EXAMPLE
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a(9)=108=3*binomial(9,2) increasing ternary 8-forest with n=9 vertices: there are three 8-forests (seven one vertex trees together with any of the three different 2-vertex trees) each with binomial(9,2)= 36 increasing labelings.
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CROSSREFS
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Cf. A132052 (seventh column).
Sequence in context: A035812 A054624 A143403 this_sequence A113853 A030248 A033535
Adjacent sequences: A132050 A132051 A132052 this_sequence A132054 A132055 A132056
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 14 2007
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