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A000405 Number of 6-level labeled rooted trees with n leaves.
(Formerly M4261 N1781)
16
1, 1, 6, 51, 561, 7556, 120196, 2201856, 45592666, 1051951026, 26740775306, 742069051906, 22310563733864, 722108667742546, 25024187820786357, 924161461265888370, 36223781285638309482, 1501552062016443881514 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
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).
LINKS
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)
FORMULA
E.g.f.: exp(exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1).
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
Column k=5 of A144150.
Sequence in context: A345259 A124565 A057817 * A113352 A063169 A346667
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Extended with new definition by Christian G. Bower, Aug 15 1998
STATUS
approved

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Last modified March 19 07:38 EDT 2024. Contains 370958 sequences. (Running on oeis4.)