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Search: id:A132055
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| 1, 165, 16665, 1349205, 97026930, 6526750230, 423076603950, 26922666320550, 1702498733310375, 107876426221438875, 6888889247523458175, 445180690239692281875, 29198763785973826044000
(list; graph; listen)
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OFFSET
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10,2
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COMMENT
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a(n), n>=10, enumerates unordered forests composed of nine plane 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.
a(n), n>=10, enumerates unordered forests composed of ten 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))^10)/10!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
E.g.f. (-1+(1-2*x)^(-1/2))^10/10!.
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EXAMPLE
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a(11)=165=3*binomial(11,2) increasing ternary 10-forest with n=11 vertices: there are three 10-forests (nine one vertex trees together with any of the three different 2-vertex trees) each with binomial(11,2)= 55 increasing labelings.
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CROSSREFS
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Cf. A132054 (eighth column).
Sequence in context: A105944 A071576 A140912 this_sequence A046178 A015982 A065210
Adjacent sequences: A132052 A132053 A132054 this_sequence A132056 A132057 A132058
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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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