login
Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n labeled nodes.
2

%I #10 Dec 16 2014 16:46:51

%S 1,1,3,52,2850,393848,125054832,88260845008,137304025714320,

%T 469859118159233792,3527181890877230433408,57833314494643038031674112,

%U 2060645597746315164145860149760,158727775101107953869596632383822848,26301662700662611321804753231934678909952

%N Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n labeled nodes.

%C Figure n3 demonstrates all 4*13=52 hierarchical orderings on n=3 connected points. In addition, the pink pictures describe the 10 cases where not all or no points are connected.

%H Alois P. Heinz, <a href="/A136723/b136723.txt">Table of n, a(n) for n = 0..76</a>

%H Thomas Wieder, <a href="/A136723/a136723_n3.pdf">Figure n3</a>

%F a(n) = A001187(n)*A000670(n);

%e There is A001187(2)=1 connected graph for n=2 labeled elements: The chain 1-2.

%e The chain gives us 3 hierarchical orderings:

%e 1-2

%e 1

%e |

%e 2

%e 2

%e |

%e 1

%Y Cf. A001187, A000670, A136722, A034691, A075729.

%K easy,nonn

%O 0,3

%A _Thomas Wieder_, Jan 19 2008; corrected Jan 19 2008

%E Offset corrected by _Alois P. Heinz_, Dec 16 2014