A132053 Eighth column of triangle A035342.

1, 108, 7470, 429660, 22629915, 1143782640, 56936699820, 2835191759400, 142610008065525, 7291723635296100, 380553986882119050, 20327650785482940900, 1113292728197378103375, 62584367768103890709000

Offset: 8

Author

Wolfdieter Lang Sep 14 2007

Keywords

• nonn
• easy

Comments

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.

Examples

			a(9)=108=3*binomial(9,2) increasing ternary 8-forest with n=9 vertices: there are three 8-forests (seven 1-vertex trees together with any of the three different 2-vertex trees) each with binomial(9,2)= 36 increasing labelings.
		

Crossrefs

Cf. A132052 (seventh column).

Formula

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!.