A001669 Number of 7-level labeled rooted trees with n leaves.
1, 1, 7, 70, 910, 14532, 274778, 5995892, 148154860, 4085619622, 124304629050, 4133867297490, 149114120602860, 5796433459664946, 241482353893283349, 10730629952953517859, 506500241174366575122, 25302666611855946733140
Offset: 0
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
Programs
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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
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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 *)
Formula
E.g.f.: exp(exp(exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)-1).
Extensions
Extended with new definition by Christian G. Bower, Aug 15 1998