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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Extended with new definition by Christian G. Bower, Aug 15 1998
STATUS
approved