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A109186
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Number of hierarchical orderings of n unlabeled elements where levels are clustered. Labeled analog 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, 7299970808014926301354, 301529053235119043206790
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
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LINKS
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FORMULA
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G.f.: exp(-(-1+exp(exp(z)-1))/(-2+exp(exp(z)-1)))-1.
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EXAMPLE
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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
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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
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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