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A136723
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Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n labeled nodes.
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2
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1, 1, 3, 52, 2850, 393848, 125054832, 88260845008, 137304025714320, 469859118159233792, 3527181890877230433408, 57833314494643038031674112, 2060645597746315164145860149760, 158727775101107953869596632383822848, 26301662700662611321804753231934678909952
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OFFSET
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0,3
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COMMENTS
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Figure n3 demonstrates all 4*13=52 hierarchical orderings on n=3 connected points. In addition, the pink pictures describe the 10 cases where not all or no points are connected.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..76
Thomas Wieder, Figure n3
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FORMULA
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a(n) = A001187(n)*A000670(n);
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EXAMPLE
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There is A001187(2)=1 connected graph for n=2 labeled elements: The chain 1-2.
The chain gives us 3 hierarchical orderings:
1-2
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2
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1
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CROSSREFS
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Cf. A001187, A000670, A136722, A034691, A075729.
Sequence in context: A301948 A337755 A263530 * A202649 A347611 A302932
Adjacent sequences: A136720 A136721 A136722 * A136724 A136725 A136726
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KEYWORD
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easy,nonn
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AUTHOR
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Thomas Wieder, Jan 19 2008; corrected Jan 19 2008
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EXTENSIONS
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Offset corrected by Alois P. Heinz, Dec 16 2014
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STATUS
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approved
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