1,4

N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.

Thomas Wieder, Home Page.

Thomas Wieder, Old Home Page.

egf = exp(-(-exp(z)+1+z)/(2-exp(z)+z))

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.

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);

Cf. A075729, A097237.

Sequence in context: A111500 A161325 A042849 this_sequence A061485 A136335 A008422

Adjacent sequences: A097233 A097234 A097235 this_sequence A097237 A097238 A097239

nonn

Thomas Wieder (wieder.thomas(AT)t-online.de), Aug 02 2004