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A000405
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Number of 6-level labeled rooted trees with n leaves.
(Formerly M4261 N1781)
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16
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1, 1, 6, 51, 561, 7556, 120196, 2201856, 45592666, 1051951026, 26740775306, 742069051906, 22310563733864, 722108667742546, 25024187820786357, 924161461265888370, 36223781285638309482, 1501552062016443881514
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OFFSET
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0,3
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REFERENCES
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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
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..150
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Jekuthiel Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]
Gottfried Helms, Bell Numbers, 2008.
T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346. (Annotated scanned copy)
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 295
Index entries for sequences related to rooted trees
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FORMULA
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E.g.f.: exp(exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1).
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A000110, A000258, A000307, A000357, A001669.
Column k=5 of A144150.
Sequence in context: A345259 A124565 A057817 * A113352 A063169 A346667
Adjacent sequences: A000402 A000403 A000404 * A000406 A000407 A000408
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Extended with new definition by Christian G. Bower, Aug 15 1998
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STATUS
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approved
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