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

1,2

Comments

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

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

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]

Example

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

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);

Crossrefs

Cf. A075729, A104525.

Cf. A104525, A083355, A075729.

Sequence in context: A075744 A277610 A261899 * A099391 A008785 A375616

Adjacent sequences: A109183 A109184 A109185 * A109187 A109188 A109189

Keyword

nonn

Author

Thomas Wieder, Jun 21 2005, Mar 29 2008

Status

approved