A001669 Number of 7-level labeled rooted trees with n leaves. (Formerly M4443 N1879)

1, 1, 7, 70, 910, 14532, 274778, 5995892, 148154860, 4085619622, 124304629050, 4133867297490, 149114120602860, 5796433459664946, 241482353893283349, 10730629952953517859, 506500241174366575122, 25302666611855946733140

Offset

0,3

References

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.

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

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]

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 296

Index entries for sequences related to rooted trees

Formula

E.g.f.: exp(exp(exp(exp(exp(exp(exp(x)-1)-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(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&, 6]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *)
With[{nn=20}, Join[{1}, Rest[CoefficientList[Series[Nest[Exp[#]-1&, Exp[x]-1, 6], {x, 0, nn}], x] Range[0, nn]!]]] (* Harvey P. Dale, Mar 02 2015 *)

Crossrefs

Cf. A000110, A000258, A000307, A000357, A000405.

Column k=6 of A144150.

Sequence in context: A113343 A124566 A141151 * A051604 A346668 A362775

Adjacent sequences: A001666 A001667 A001668 * A001670 A001671 A001672

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Extended with new definition by Christian G. Bower, Aug 15 1998

Status

approved