OFFSET
1,4
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
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)!.
EXAMPLE
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}.
MATHEMATICA
Table[Exp[n]*Gamma[n-2, n] // Round, {n, 1, 50}] (* Jean-François Alcover, Jan 15 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
David Callan, Mar 30 2007
STATUS
approved