A000357 Number of 5-level labeled rooted trees with n leaves. (Formerly M3979 N1648)

1, 1, 5, 35, 315, 3455, 44590, 660665, 11035095, 204904830, 4183174520, 93055783320, 2238954627848, 57903797748386, 1601122732128779, 47120734323344439, 1470076408565099152, 48449426629560437576, 1681560512531504058350, 61293054886119796799892

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

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..400

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. (Annotated scanned copy)

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 294

Index entries for sequences related to rooted trees

Formula

E.g.f.: exp(exp(exp(exp(exp(x)-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(1)))): seq(a(n), n=0..30);  # Alois P. Heinz, Sep 11 2008

Mathematica

max = 17; Join[{1}, MatrixPower[Array[StirlingS2, {max, max}], 5][[All, 1]]] (* Jean-François Alcover, Mar 03 2014 *)

Crossrefs

a(n)=|A039813(n,1)| (first column of triangle).

Cf. A000110, A000258, A000307, A000405, A001669.

Column k=4 of A144150.

Sequence in context: A225177 A151344 A015683 * A102147 A051577 A124564

Adjacent sequences: A000354 A000355 A000356 * A000358 A000359 A000360

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved