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%I #11 May 11 2016 10:30:11
%S 1,1,9,117,1989,41709,1038975,29947185,979687005,35839643175,
%T 1449091813035,64144495494825,3084209792570721,160023238477245789,
%U 8909102551102555002,529651263967161225648,33482356679629151295651
%N Number of 9-level labeled rooted trees with n leaves.
%D J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.
%D T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
%H Alois P. Heinz, <a href="/A081629/b081629.txt">Table of n, a(n) for n = 0..150</a>
%F E.g.f.: exp(exp(exp(exp(exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)-1)-1)-1).
%o (PARI) a(n)=local(X); if(n<0,0,X=x+x*O(x^n); n!*polcoeff(exp(exp(exp(exp(exp(exp(exp(exp(exp(X)-1)-1)-1)-1)-1)-1)-1)-1),n)).
%Y Cf. A000110, A000258, A000307, A000357, A001669.
%Y Column k=8 of A144150.
%K nonn
%O 0,3
%A _Benoit Cloitre_, Apr 23 2003
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