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A097236
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Number of hierachical orderings ("societies") with at least 2 elements ("individuals") on each level for n labeled elements.
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2
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0, 1, 1, 10, 31, 271, 1534, 14393, 117653, 1253524, 13140557, 160679069
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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)+1+z)/(2-exp(z)+z))
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EXAMPLE
| a(4) = 10. 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 = 4 and x = 2 one has 1234; 12:34; 13:24; 14:23; 12|34; 31|42;
43|21; 24|13; 21|34; 43|12; which gives 10 different hierachical
societies with at least 2 labeled individuals per level.
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MAPLE
| with(combstruct); SetSeqSetxL:=[T, {T=Set(S), S=Sequence(U, card>=1), U=Set(Z, card >= 2)}, labeled]; #where x is an integer 1, 2, 3, ... # x=2 gives 2 individuals per level. seq(count(SetSeqSet2L, size=j), j=1..12);
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CROSSREFS
| Cf. A075729, A097237.
Sequence in context: A161325 A187705 A042849 * A061485 A136335 A008422
Adjacent sequences: A097233 A097234 A097235 * A097237 A097238 A097239
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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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