OFFSET
1,3
COMMENTS
This problem might arise if there was only a two-person boat available.
Also the number of ranked tree-child networks. - Michael Fuchs, May 29 2021
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..190
Francois Bienvenu, Amaury Lambert, and Mike Steel, Combinatorial and stochastic properties of ranked tree-child networks, arXiv:2007.09701 [math.PR], 2021.
Alessandra Caraceni, Michael Fuchs, and Guan-Ru Yu, Bijections for ranked tree-child networks, arXiv:2105.10137 [math.CO], 2021.
FORMULA
a(n) = n!*((n-1)!)^2/((2!)^(n-1)).
a(n) ~ 4*sqrt(2)*Pi^(3/2)*n^(3*n-1/2)/(2^n*exp(3*n)). - Ilya Gutkovskiy, Dec 17 2016
EXAMPLE
For n=3 there are 6 ways. Let a,b,c start on one side. We have:
1) Send (a,b), return(a), send(a,c);
2) Send (a,b), return(b), send(b,c);
3) Send (b,c), return(b), send(a,b);
4) Send (b,c), return(c), send(a,c);
5) Send (a,c), return(a), send(a,b);
6) Send (a,c), return(c), send(b,c).
MATHEMATICA
f[n_] := n! (n - 1)!^2/2^(n - 1); Array[f, 15] (* Robert G. Wilson v, Dec 17 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ron Smith (ron.smith(AT)henryschein.com), Nov 04 2009
EXTENSIONS
a(13) and a(14) corrected by Ilya Gutkovskiy, Dec 17 2016
More terms from Ilya Gutkovskiy, Dec 18 2016
STATUS
approved