2,2

Contribution from Olivier GERARD (olivier.gerard(AT)gmail.com), Mar 25 2009: (Start)

a(n) is the number of hierarchical partitions of a set of n elements into two second level classes : k>1 subsets of [n] are further grouped in two classes.

a(n) is equivalently the number of trees of uniform height 3 with n labelled leaves, and a root of order two. (End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

R. Fray, A generating function associated with the generalized Stirling numbers, Fib. Quart. 5 (1967), 356-366.

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.

E.g.f.: 1/2*(exp(exp(x)-1)-1)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 28 2003

a(n) = sum( stirlingS2(n,k)*stirlingS2(k,2), k=0..n) [From Olivier GERARD (olivier.gerard(AT)gmail.com), Mar 25 2009]

a(2) = 1, since there is only one partition of {1,2} into two classes, and only one way to partition those classes. a(4)=32=7*1+6*3+1*7 since there are 7 ways of partitionning {1,2,3,4} into two classes (which cannot be grouped further), 6 ways of partitioning a set of 4 elements into three classes and three ways to partition three classes into two super-classes, etc. [From Olivier GERARD (olivier.gerard(AT)gmail.com), Mar 25 2009]

Cf. A000559, A046817.

Cf. A001861 for the related bicolor set partitions. [From Olivier GERARD (olivier.gerard(AT)gmail.com), Mar 25 2009]

Sequence in context: A084326 A137637 A125190 this_sequence A047763 A026993 A121965

Adjacent sequences: A000555 A000556 A000557 this_sequence A000559 A000560 A000561

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jan 13, 2000.