A132052 Seventh column of triangle A035342.

1, 84, 4662, 220500, 9740115, 419625360, 18048090060, 785470565880, 34872721208325, 1587323312675100, 74301594199682850, 3583275362669702700, 178220792065162821975, 9146316814629741747000, 484394828691800237211000

Offset: 7

Author

Wolfdieter Lang Sep 14 2007

Keywords

• nonn
• easy

Comments

a(n), n >= 7, enumerates unordered forests composed of seven 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(8)=84=3*binomial(8,2) increasing ternary 7-forest with n=8 vertices: there are three 7-forests (six 1-vertex trees together with any of the three different 2-vertex trees) each with binomial(8,2)= 28 increasing labelings.
		

Crossrefs

Cf. A132051 (sixth column).

Formula

E.g.f.: ((x*c(x/2)*(1-2*x)^(-1/2))^7)/7!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.

E.g.f.: (-1+(1-2*x)^(-1/2))^7/7!.