proposed

approved

editing

proposed

E.g.f. : ((x*c(x/2)*(1-2*x)^(-1/2))^10)/10!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.

E.g.f. : (-1+(1-2*x)^(-1/2))^10/10!.

approved

editing

_Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) _ Sep 14 2007

Tenth column of triangle A035342.

1, 165, 16665, 1349205, 97026930, 6526750230, 423076603950, 26922666320550, 1702498733310375, 107876426221438875, 6888889247523458175, 445180690239692281875, 29198763785973826044000

10,2

a(n), n>=10, enumerates unordered forests composed of nine plane 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.

a(n), n>=10, enumerates unordered forests composed of ten 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.

E.g.f. ((x*c(x/2)*(1-2*x)^(-1/2))^10)/10!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.

E.g.f. (-1+(1-2*x)^(-1/2))^10/10!.

a(11)=165=3*binomial(11,2) increasing ternary 10-forest with n=11 vertices: there are three 10-forests (nine one vertex trees together with any of the three different 2-vertex trees) each with binomial(11,2)= 55 increasing labelings.

Cf. A132054 (eighth column).

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 14 2007

approved