cp's OEIS Frontend

A136723 Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n labeled nodes.

%I A136723 #10 Dec 16 2014 16:46:51
%S A136723 1,1,3,52,2850,393848,125054832,88260845008,137304025714320,
%T A136723 469859118159233792,3527181890877230433408,57833314494643038031674112,
%U A136723 2060645597746315164145860149760,158727775101107953869596632383822848,26301662700662611321804753231934678909952
%N A136723 Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n labeled nodes.
%C A136723 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 A136723 Alois P. Heinz, <a href="/A136723/b136723.txt">Table of n, a(n) for n = 0..76</a>
%H A136723 Thomas Wieder, <a href="/A136723/a136723_n3.pdf">Figure n3</a>
%F A136723 a(n) = A001187(n)*A000670(n);
%e A136723 There is A001187(2)=1 connected graph for n=2 labeled elements: The chain 1-2.
%e A136723 The chain gives us 3 hierarchical orderings:
%e A136723 1-2
%e A136723 1
%e A136723 |
%e A136723 2
%e A136723 2
%e A136723 |
%e A136723 1
%Y A136723 Cf. A001187, A000670, A136722, A034691, A075729.
%K A136723 easy,nonn
%O A136723 0,3
%A A136723 _Thomas Wieder_, Jan 19 2008; corrected Jan 19 2008
%E A136723 Offset corrected by _Alois P. Heinz_, Dec 16 2014