A129137 Number of trees on [n], rooted at 1, in which 2 is a descendant of 3.

0, 0, 1, 5, 37, 366, 4553, 68408, 1206405, 24447440, 560041201, 14315792256, 404057805989, 12482986261760, 419042630871225, 15189786100468736, 591374264243364037, 24612549706061862912, 1090556290466098198625

Offset: 1

Author

David Callan, Mar 30 2007

Keywords

• nonn

Examples

			a(4)=5 counts {1->3->2, 1->4}, {1->3->2, 3->4}, {1->3->2->4}, {1->3->4->2}, {1->4->3->2}.
		

Links

• Washington G. Bomfim, Table of n, a(n) for n = 1..50
• H. Bergeron, E. M. F. Curado, J. P. Gazeau and L. M. C. S. Rodrigues, A note about combinatorial sequences and Incomplete Gamma function, arXiv preprint arXiv: 1309.6910, 2013

Crossrefs

Cf. A057500 = binomial(n-1, 2)*a(n).

Programs

Mathematica

Table[Exp[n]*Gamma[n-2, n] // Round, {n, 1, 50}] (* Jean-François Alcover, Jan 15 2014 *)

Formula

The following formula counts these trees by the length r of the path from 1 to 3: Sum_{r=1..n-2} (n-3)!*n^(n-2-r)/(n-2-r)!.