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A109186
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Number of hierarchical orderings of n unlabeled elements where levels are clustered. Labeled analogue of A104525.
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3
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1, 5, 36, 340, 3968, 55045, 883578, 16092772, 327632793, 7369013917, 181373908752, 4847134062319, 139729893353690, 4320778186663065, 142630863311312977, 5005242986601625051, 186036975046460920033
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A109186 is the exp transform of A083355. [From Thomas Wieder (thomas.wieder(AT)t-online.de), Sep 12 2008]
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REFERENCES
| N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
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LINKS
| Thomas Wieder, Discussion of A109186
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FORMULA
| Generating function = 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 (thomas.wieder(AT)t-online.de), Sep 12 2008]
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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}].
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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);
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CROSSREFS
| Cf. A075729, A104525.
Cf. A104525, A083355, A075729.
Sequence in context: A127132 A141764 A075744 * A099391 A008785 A081918
Adjacent sequences: A109183 A109184 A109185 * A109187 A109188 A109189
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KEYWORD
| nonn
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AUTHOR
| Thomas Wieder (wieder.thomas(AT)t-online.de), Jun 21 2005, Mar 29 2008
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