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%I M4261 N1781 #54 Aug 06 2018 14:55:47
%S 1,1,6,51,561,7556,120196,2201856,45592666,1051951026,26740775306,
%T 742069051906,22310563733864,722108667742546,25024187820786357,
%U 924161461265888370,36223781285638309482,1501552062016443881514
%N Number of 6-level labeled rooted trees with n leaves.
%D J. de la Cal, J. Carcamo, Set partitions and moments of random variables, J. Math. Anal. Applic. 378 (2011) 16 doi:10.1016/j.jmaa.2011.01.002 Remark 5
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A000405/b000405.txt">Table of n, a(n) for n = 0..150</a>
%H P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H Jekuthiel Ginsburg, <a href="/A000405/a000405.pdf">Iterated exponentials</a>, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]
%H Gottfried Helms, <a href="http://go.helms-net.de/math/binomial/04_5_SummingBellStirling.pdf">Bell Numbers</a>, 2008.
%H T. Hogg and B. A. Huberman, <a href="http://dx.doi.org/10.1103/PhysRevA.32.2338 ">Attractors on finite sets: the dissipative dynamics of computing structures</a>, Phys. Review A 32 (1985), 2338-2346.
%H T. Hogg and B. A. Huberman, <a href="/A000258/a000258.pdf">Attractors on finite sets: the dissipative dynamics of computing structures</a>, Phys. Review A 32 (1985), 2338-2346. (Annotated scanned copy)
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=295">Encyclopedia of Combinatorial Structures 295</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F E.g.f.: exp(exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1).
%p 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(g(g(1))))): seq(a(n), n=0..30); # _Alois P. Heinz_, Sep 11 2008
%t g[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, (n-1)!*Sum[p[k]*b[n-k]/(k-1)!/(n-k)!, {k, 1, n}]]; b]; a = Nest[g, 1&, 5]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 12 2014, after _Alois P. Heinz_ *)
%Y Cf. A000110, A000258, A000307, A000357, A001669.
%Y Column k=5 of A144150.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E Extended with new definition by _Christian G. Bower_, Aug 15 1998
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