A000405 Number of 6-level labeled rooted trees with n leaves. (Formerly M4261 N1781)

1, 1, 6, 51, 561, 7556, 120196, 2201856, 45592666, 1051951026, 26740775306, 742069051906, 22310563733864, 722108667742546, 25024187820786357, 924161461265888370, 36223781285638309482, 1501552062016443881514

Offset

0,3

References

J. de la Cal, J. Carcamo, Set partitions and moments of random variables, J. Math. Anal. Applic. 378 (2011) 16 doi:10.1016/j.jmaa.2011.01.002 Remark 5

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]

Gottfried Helms, Bell Numbers, 2008.

T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.

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 295

Index entries for sequences related to rooted trees

Formula

E.g.f.: exp(exp(exp(exp(exp(exp(x)-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(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&, 5]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 12 2014, after Alois P. Heinz *)

Crossrefs

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

Column k=5 of A144150.

Sequence in context: A345259 A124565 A057817 * A113352 A063169 A346667

Adjacent sequences: A000402 A000403 A000404 * A000406 A000407 A000408

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved