A035520 Fourth column of triangle A035342; related to A045894.

0, 0, 0, 1, 30, 705, 15960, 370125, 8998290, 231416325, 6314962500, 182894567625, 5615811951750, 182497749258825, 6264206330382000, 226636350724909125, 8624703350821808250, 344535241891693978125, 14419858385821910521500

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

a(n) = A035342(n,4).

a(n), n>=4, enumerates unordered n-vertex forests composed of four plane (ordered) increasingly labeled ternary (3-ary) trees. 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(5)=30 increasing ternary 4-forest with n=5 vertices: there are three such 4-forests (three one vertex trees together with any of the three different 2-vertex trees) each with 10 increasing labelings. _Wolfdieter Lang_, Sep 14 2007.
		

Crossrefs

Cf. A035342, A045894.

Formula

a(n) = n!*A045894(n-4)/(4!*2^(n-4)), n >= 4; E.g.f. ((x*c(x/2)/(1-2*x)^(1/2))^4)/4!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.