cp's OEIS Frontend

A109186 Number of hierarchical orderings of n unlabeled elements where levels are clustered. Labeled analog of A104525.

%I A109186 #15 Jul 10 2015 19:54:09
%S A109186 1,5,36,340,3968,55045,883578,16092772,327632793,7369013917,
%T A109186 181373908752,4847134062319,139729893353690,4320778186663065,
%U A109186 142630863311312977,5005242986601625051,186036975046460920033,7299970808014926301354,301529053235119043206790
%N A109186 Number of hierarchical orderings of n unlabeled elements where levels are clustered. Labeled analog of A104525.
%C A109186 A109186 is the exp transform of A083355. [From _Thomas Wieder_, Sep 12 2008]
%D A109186 N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
%H A109186 Alois P. Heinz, <a href="/A109186/b109186.txt">Table of n, a(n) for n = 1..150</a>
%H A109186 Thomas Wieder, <a href="/A109186/a109186.txt">Discussion of A109186</a>
%F A109186 G.f.: exp(-(-1+exp(exp(z)-1))/(-2+exp(exp(z)-1)))-1.
%F A109186 a(n) = sum_{k=1}^{n} C(n-1,k-1) A083355 a(n-k) and a(0)=1. [From _Thomas Wieder_, Sep 12 2008]
%e A109186 a(2) = 5 because [a_{1}a_{2}], [a_{1}]:[a_{2}], [a_{2}]:[a_{1}], [a_{1}]|[a_{2}], [a_{1}][a_{2}].
%p A109186 Test := [T, {T=Set(S,card>=1), S=Sequence(Set(U,card>=1),card>=1), U=Set(Z,card>=1)}, labeled]; seq(count(Test,size=j),j=1..20);
%Y A109186 Cf. A075729, A104525.
%Y A109186 Cf. A104525, A083355, A075729.
%K A109186 nonn
%O A109186 1,2
%A A109186 _Thomas Wieder_, Jun 21 2005, Mar 29 2008