0,3

Number of 3-level labeled rooted trees with n leaves. - Christian G. Bower (bowerc(AT)usa.net), Aug 15 1998

Number of pairs of set partitions (d,d') of [n] such that d is finer than d'. - A. Joseph Kennedy (kennedy_2001in(AT)yahoo.co.in), Feb 05 2006

In the Comm. Algebra paper cited, I introduce a sequence of algebras called 'class partition algebras' with this sequence as dimensions. The algebras are the centralizers of wreath product in combinatorial representation theory. - A. Joseph Kennedy (kennedy_2001in(AT)yahoo.co.in), Feb 17 2008

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).

J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.

T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.

A. Joseph Kennedy, Class partition algebras as centralizer algebras, Communications in Algebra, 35 (2007), 145-170, see page 153.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.4.

T. D. Noe, Table of n, a(n) for n=0..100

P. Blasiak, A. Horzela, K. A. Penson, G.H.E. Duchamp and A. I. Solomon, Boson normal ordering via substitutions and Sheffer-type polynomials

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

P. J. Cameron, D. A. Gewurz and F. Merola, Product action, Discrete Math., 308 (2008), 386-394.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 70

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 292

K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem [J. Phys. A 37 (2004), 3475-3487]

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

Index entries for sequences related to rooted trees

Gottfried Helms, Bell Numbers, 2008.

Sum(stirling2(n, k)*(bell(k)), k=0..n). - Detlef Pauly (dettodet(AT)yahoo.de), Jun 06 2002

Representation as an infinite series (Dobinski-type formula), in Maple notation: a(n)=exp(exp(-1)-1)*sum(evalf(sum(p!*stirling2(k, p)*exp(-p), p=1..k))*k^n/k!, k=0..infinity), n=1, 2.... - Karol A. Penson (penson(AT)lptl.jussieu.fr), Nov 28 2003.

a(n)=sum_{k=0..n) A055896(n,k). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2008

with(combinat, bell, stirling2): seq(add(stirling2(n, k)*(bell(k)), k=0..n), n=0..30);

with(combstruct); SetSetSetL := [T, {T=Set(S), S=Set(U, card >= 1), U=Set(Z, card >=1)}, labeled];

NestList[ Factor[ D[ #1, x ] ]&, Exp[ Exp[ Exp[ x-1 ]-1 ]-1 ], n ] /. (x->1)

a(n)=|A039811(n, 1)| (first column of triangle). Cf. A000110, A000307, A000357, A000405, A001669.

Row sums of (Stirling2)^2 triangle A130191.

Sequence in context: A096471 A140097 A105227 this_sequence A070863 A062569 A089057

Adjacent sequences: A000255 A000256 A000257 this_sequence A000259 A000260 A000261

nonn,easy,nice

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