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A132054 Ninth column of triangle A035342. 1
1, 135, 11385, 782595, 48455550, 2839726890, 162006594750, 9153448954650, 517901415206175, 29561484489161625, 1710820788894392175, 100736227863519373125, 6049367893509827386500, 371102130337105087420500 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

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.

LINKS

Table of n, a(n) for n=9..22.

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!.

EXAMPLE

a(10)=135=3*binomial(10,2) increasing ternary 9-forest with n=10 vertices: there are three 9-forests (eight 1-vertex trees together with any of the three different 2-vertex trees) each with binomial(10,2)= 45 increasing labelings.

CROSSREFS

Cf. A132053 (eighth column).

Sequence in context: A143404 A051028 A076011 * A273440 A106175 A203625

Adjacent sequences: A132051 A132052 A132053 * A132055 A132056 A132057

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang Sep 14 2007

STATUS

approved

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Last modified February 7 12:58 EST 2023. Contains 360123 sequences. (Running on oeis4.)