0,3

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.

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

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 293

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]

Index entries for sequences related to rooted trees

K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem

Gottfried Helms, Bell Numbers, 2008.

E.g.f.: exp(exp(exp(exp(x)-1)-1)-1).

g:= proc(p) local b; b:=proc(n) option remember; if n=0 then 1 else (n-1)! *add (p(k)*b(n-k)/ (k-1)!/ (n-k)!, k=1..n) fi end end: a:= g(g(g(1))): seq (a(n), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 11 2008]

a(n)=|A039812(n, 1)| (first column of triangle). Cf. A000110, A000258, A000357, A000405, A001669.

Adjacent sequences: A000304 A000305 A000306 this_sequence A000308 A000309 A000310

Sequence in context: A039304 A152404 A062817 this_sequence A049376 A083410 A052772

nonn,easy

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

Extended with new definition by Christian G. Bower (bowerc(AT)usa.net), Aug 15 1998.