login
Seventh column of triangle A035342.
1

%I #5 Jan 05 2021 22:05:24

%S 1,84,4662,220500,9740115,419625360,18048090060,785470565880,

%T 34872721208325,1587323312675100,74301594199682850,

%U 3583275362669702700,178220792065162821975,9146316814629741747000,484394828691800237211000

%N Seventh column of triangle A035342.

%C 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.

%F 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.

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

%e 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.

%Y Cf. A132051 (sixth column).

%K nonn,easy

%O 7,2

%A _Wolfdieter Lang_ Sep 14 2007