%I A000307 M3590 N1455
%S A000307 1,1,4,22,154,1304,12915,146115,1855570,26097835,402215465,6734414075,
%T A000307 121629173423,2355470737637,48664218965021,1067895971109199,
%U A000307 24795678053493443,607144847919796830,15630954703539323090
%N A000307 Number of 4-level labeled rooted trees with n leaves.
%D A000307 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000307 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000307 J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
%D A000307 T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative 
               dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
%D A000307 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Example 5.2.4.
%H A000307 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A000307 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=293">
               Encyclopedia of Combinatorial Structures 293</a>
%H A000307 K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, <a 
               href="http://arXiv.org/abs/quant-ph/0312202">Hierarchical Dobinski-type 
               relations via substitution and the moment problem</a> [J. Phys. A 
               37 (2004), 3475-3487]
%H A000307 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A000307 K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, <a 
               href="http://arXiv.org/abs/quant-ph/0312202">Hierarchical Dobinski-type 
               relations via substitution and the moment problem</a>
%H A000307 Gottfried Helms, <a href="http://go.helms-net.de/math/binomial/04_5_SummingBellStirling.pdf">
               Bell Numbers</a>, 2008.
%F A000307 E.g.f.: exp(exp(exp(exp(x)-1)-1)-1).
%p A000307 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]
%Y A000307 a(n)=|A039812(n, 1)| (first column of triangle). Cf. A000110, A000258, 
               A000357, A000405, A001669.
%Y A000307 Sequence in context: A039304 A152404 A062817 this_sequence A049376 A083410 
               A052772
%Y A000307 Adjacent sequences: A000304 A000305 A000306 this_sequence A000308 A000309 
               A000310
%K A000307 nonn,easy
%O A000307 0,3
%A A000307 N. J. A. Sloane (njas(AT)research.att.com).
%E A000307 Extended with new definition by Christian G. Bower (bowerc(AT)usa.net), 
               Aug 15 1998.