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 A167484 For n people on one side of a river, the number of ways they can all travel to the opposite side following the pattern of 2 sent, 1 returns, 2 sent, 1 returns, ..., 2 sent. 4
 1, 1, 6, 108, 4320, 324000, 40824000, 8001504000, 2304433152000, 933295426560000, 513312484608000000, 372664863825408000000, 348814312540581888000000, 412647331735508373504000000, 606591577651197309050880000000, 1091864839772155156291584000000000, 2375897891344209620090486784000000000 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A010563 A114310 A221954 * A011555 A122722 A127946 Adjacent sequences: A167481 A167482 A167483 * A167485 A167486 A167487 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

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Last modified December 2 07:06 EST 2022. Contains 358493 sequences. (Running on oeis4.)