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

1, 5, 36, 340, 3968, 55045, 883578, 16092772, 327632793, 7369013917, 181373908752, 4847134062319, 139729893353690, 4320778186663065, 142630863311312977, 5005242986601625051, 186036975046460920033, 7299970808014926301354, 301529053235119043206790

Offset: 1

Author

Thomas Wieder, Jun 21 2005, Mar 29 2008

Keywords

• nonn

Comments

A109186 is the exp transform of A083355. [From Thomas Wieder, Sep 12 2008]

Examples

			a(2) = 5 because [a_{1}a_{2}], [a_{1}]:[a_{2}], [a_{2}]:[a_{1}], [a_{1}]|[a_{2}], [a_{1}][a_{2}].
		

References

• N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..150
• Thomas Wieder, Discussion of A109186

Crossrefs

Cf. A075729, A104525.

Cf. A104525, A083355, A075729.

Programs

Maple

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);

Formula

G.f.: exp(-(-1+exp(exp(z)-1))/(-2+exp(exp(z)-1)))-1.

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]