login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005754 Number of planted identity matched trees with n nodes.
(Formerly M1765)
3
1, 1, 2, 7, 24, 95, 388, 1650, 7183, 31965, 144502, 662241, 3068942, 14358678, 67729973, 321759461, 1538076291, 7392775328, 35707198905, 173221206284, 843634142771, 4123376617009, 20218897206392, 99436453714990, 490355165178472, 2424146632435852 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of rooted identity trees with n nodes and edges not attached to root are 2-colored or oriented. - Christian G. Bower, Dec 15 1999

REFERENCES

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 = 1..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 430

R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1991), 93-104.

R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1981), 97. (Annotated scanned copy)

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

FORMULA

a(n+1) is Weigh transform of A005753. - Christian G. Bower, Dec 15 1999

a(n) ~ c * d^n / n^(3/2), where d = A246312 = 5.2490324912281705791649522..., c = 0.05927840588836202377824646... . - Vaclav Kotesovec, Aug 25 2014

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

add(binomial(2*b((i-1)$2), j)*b(n-i*j, i-1), j=0..n/i)))

end:

g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

add(binomial(b((i-1)$2), j)*g(n-i*j, i-1), j=0..n/i)))

end:

a:= n-> g((n-1)$2):

seq(a(n), n=1..30); # Alois P. Heinz, Aug 01 2013

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[2*b[i-1, i-1], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; g[n_, i_] := g[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[b[i-1, i-1], j]*g[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := g[n-1, n-1]; Table[a[n], {n, 1, 30}] // FullSimplify (* Jean-François Alcover, Dec 02 2013, translated from Alois P. Heinz's Maple program *)

CROSSREFS

Cf. A005753, A102755, A246312.

Sequence in context: A150421 A150422 A137952 * A007162 A150423 A150424

Adjacent sequences: A005751 A005752 A005753 * A005755 A005756 A005757

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 16:20 EST 2022. Contains 358431 sequences. (Running on oeis4.)