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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052320 Number of labeled trimmed trees with n nodes. 1
1, 1, 1, 0, 4, 5, 96, 1057, 14848, 235881, 4234240, 84815621, 1877090304, 45524670061, 1201345331200, 34283233751145, 1052350187831296, 34582597023733073, 1211614017182760960, 45088964565749965837 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A trimmed tree is a tree with a forbidden limb of length 2.

A tree with a forbidden limb of length k is a tree where the path from any leaf inward hits a branching node or another leaf within k steps.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for sequences related to trees

FORMULA

E.g.f.: 1 + x^3/2 + x^4/2 + B(x) - B(x)^2/2 where B(x) is e.g.f. of A052318.

a(n) ~ (1+LambertW(-2*exp(-2)))^(3/2) * exp((n*LambertW(-2*exp(-2)))/2) * n^(n-2). - Vaclav Kotesovec, Mar 29 2014

MATHEMATICA

CoefficientList[Series[1+x^3/2+x^4/2-LambertW[-x/E^(x^2)]-(LambertW[-x/E^(x^2)])^2/2, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Mar 29 2014 *)

CROSSREFS

Cf. A002955, A002988-A002992, A052318-A052329.

Sequence in context: A078985 A041173 A005512 * A079197 A113942 A073129

Adjacent sequences:  A052317 A052318 A052319 * A052321 A052322 A052323

KEYWORD

nonn

AUTHOR

Christian G. Bower, Dec 15 1999

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 09:03 EST 2019. Contains 329144 sequences. (Running on oeis4.)