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A097237
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Number of hierarchical orderings ("societies") of n labeled elements ("individuals") with at least two occupied levels.
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5
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0, 2, 12, 86, 780, 8462, 106092, 1507046, 23905740, 418581662, 8014481772, 166501716086
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
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FORMULA
| egf = exp(-(exp(z)^2-2*exp(z)+1)/(-2+exp(z)))
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EXAMPLE
| a(3) = 12. Let : denote the partition of n labeled individuals 1,2,3,4 into
x=2 sets (i.e. "societies"). E.g. in 12:34 one has a single society
with members 1 and 2 and a further single society with members 3 and 4.
Let | denote a higher level (within a single society), e.g. in 1|2 the
individual 2 is one level up with respect to individual 1. The order of
indiviuals on a level is insignificant, eg. 12|34 is equivalent to
21|43. For n = 3 and x = 2 one has
12|3; 23|1; 13|2; 1|23; 2|13; 3|12; 1|2|3; 2|3|1; 3|1|2; 1|3|2; 3|2|1;
2|1|3;
which gives 12 different societies with at least 2 occupied levels.
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MAPLE
| with(combstruct); SetSeq2SetL:=[T, {T=Set(S), S=Sequence(U, card>=2), U=Set(Z, card >= 1)}, labeled]; #where x is an integer 1, 2, 3, ... # x=2 gives 2 levels per society. seq(count(SetSeq2SetL, size=j), j=1..12);
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CROSSREFS
| Cf. A075729, A097236.
Sequence in context: A052887 A052867 A179495 * A055531 A181345 A193125
Adjacent sequences: A097234 A097235 A097236 * A097238 A097239 A097240
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KEYWORD
| nonn
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AUTHOR
| Thomas Wieder (wieder.thomas(AT)t-online.de), Aug 02 2004
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