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A132054
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Ninth column of triangle A035342.
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1
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1, 135, 11385, 782595, 48455550, 2839726890, 162006594750, 9153448954650, 517901415206175, 29561484489161625, 1710820788894392175, 100736227863519373125, 6049367893509827386500, 371102130337105087420500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 9,2
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COMMENTS
| a(n), n>=9, enumerates unordered forests composed of nine 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
| E.g.f. ((x*c(x/2)*(1-2*x)^(-1/2))^9)/9!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
E.g.f. (-1+(1-2*x)^(-1/2))^9/9!.
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EXAMPLE
| a(10)=135=3*binomial(10,2) increasing ternary 9-forest with n=10 vertices: there are three 9-forests (eight one vertex trees together with any of the three different 2-vertex trees) each with binomial(10,2)= 45 increasing labelings.
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CROSSREFS
| Cf. A132053 (eighth column).
Sequence in context: A143404 A051028 A076011 * A106175 A203625 A051307
Adjacent sequences: A132051 A132052 A132053 * A132055 A132056 A132057
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 14 2007
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