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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000307 Number of 4-level labeled rooted trees with n leaves.
(Formerly M3590 N1455)
16
1, 1, 4, 22, 154, 1304, 12915, 146115, 1855570, 26097835, 402215465, 6734414075, 121629173423, 2355470737637, 48664218965021, 1067895971109199, 24795678053493443, 607144847919796830, 15630954703539323090, 421990078975569031642, 11918095123121138408128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.

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).

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.4.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..440

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.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 293

K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem [J. Phys. A 37 (2004), 3475-3487]

Index entries for sequences related to rooted trees

K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem

Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565

FORMULA

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

a(n) = sum(sum(sum(stirling2(n,k) *stirling2(k,m) *stirling2(m,r), k=m..n), m=r..n), r=1..n), n>0. - Vladimir Kruchinin, Sep 08 2010

MAPLE

g:= proc(p) local b; b:= proc(n) option remember; `if`(n=0, 1, (n-1)! *add(p(k)*b(n-k)/ (k-1)!/ (n-k)!, k=1..n)) end end: a:= g(g(g(1))): seq(a(n), n=0..30);  # Alois P. Heinz, Sep 11 2008

MATHEMATICA

nn = 18; a = Exp[Exp[x] - 1]; b = Exp[a - 1];

Range[0, nn]! CoefficientList[Series[Exp[b - 1], {x, 0, nn}], x]  (*Geoffrey Critzer, Dec 28 2011*)

CROSSREFS

a(n)=|A039812(n,1)| (first column of triangle).

Cf. A000110, A000258, A000357, A000405, A001669.

Column k=3 of A144150.

Sequence in context: A152404 A062817 A196275 * A049376 A083410 A052772

Adjacent sequences:  A000304 A000305 A000306 * A000308 A000309 A000310

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Extended with new definition 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 June 27 11:25 EDT 2017. Contains 288788 sequences.