login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000357 Number of 5-level labeled rooted trees with n leaves.
(Formerly M3979 N1648)
16
1, 1, 5, 35, 315, 3455, 44590, 660665, 11035095, 204904830, 4183174520, 93055783320, 2238954627848, 57903797748386, 1601122732128779, 47120734323344439, 1470076408565099152, 48449426629560437576, 1681560512531504058350, 61293054886119796799892 (list; graph; refs; listen; history; text; internal format)
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..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]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 294

Index entries for sequences related to rooted trees

Gottfried Helms, Bell Numbers, 2008.

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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 3 21:14 EST 2016. Contains 278745 sequences.