A132054 Ninth column of triangle A035342.

1, 135, 11385, 782595, 48455550, 2839726890, 162006594750, 9153448954650, 517901415206175, 29561484489161625, 1710820788894392175, 100736227863519373125, 6049367893509827386500, 371102130337105087420500

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