A081629 Number of 9-level labeled rooted trees with n leaves.

1, 1, 9, 117, 1989, 41709, 1038975, 29947185, 979687005, 35839643175, 1449091813035, 64144495494825, 3084209792570721, 160023238477245789, 8909102551102555002, 529651263967161225648, 33482356679629151295651

Offset: 0

Author

Benoit Cloitre, Apr 23 2003

Keywords

• nonn

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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A000110, A000258, A000307, A000357, A001669.

Column k=8 of A144150.

Programs

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))

Formula

E.g.f.: exp(exp(exp(exp(exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)-1)-1)-1).