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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007856 Subtrees in rooted plane trees on n nodes. 2
1, 3, 12, 52, 236, 1109, 5366, 26639, 135300, 701269, 3700400, 19834973, 107784622, 592705377, 3292970302, 18458954896, 104276682820, 593056996445, 3392898090908, 19512100041995, 112729617387020, 653965783541960, 3807766434556940 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

G.-S. Cheon, H. Kim, L. W. Shapiro, Mutation effects in ordered trees, arXiv preprint arXiv:1410.1249 [math.CO], 2014.

M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.

Index entries for sequences related to rooted trees

FORMULA

G.f.: (1/8) * (1 + 1/sqrt(1-4*x)) * (1 + sqrt(1-4*x) - sqrt(2) * sqrt(1 - 10*x + sqrt(1-4*x))), see Klazar's paper. - Sean A. Irvine, Feb 06 2018

a(n) = ((n - 1)/2)*CatalanNumber(n-1)*(1 - hypergeom([-1/2, -n], [n - 1], -4)). - Peter Luschny, Aug 04 2019

MATHEMATICA

Rest[CoefficientList[Series[(1/8) (1 + 1/Sqrt[1 - 4  x]) (1 + Sqrt[1 - 4  x] - Sqrt[2]  Sqrt[1 - 10  x + Sqrt[1 - 4  x]]), {x, 0, 33}], x]] (* Vincenzo Librandi, Feb 07 2018 *)

A007856[n_] := ((n-1)/2) CatalanNumber[n-1](1 - Hypergeometric2F1[-1/2, - n, n-1, -4]); Table[A007856[n], {n, 1, 23}] (* Peter Luschny, Aug 04 2019 *)

CROSSREFS

Sequence in context: A151193 A151194 A268208 * A151195 A151196 A010736

Adjacent sequences:  A007853 A007854 A007855 * A007857 A007858 A007859

KEYWORD

nonn

AUTHOR

Martin Klazar

EXTENSIONS

More terms from Sean A. Irvine, Feb 06 2018

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 December 14 14:20 EST 2019. Contains 329979 sequences. (Running on oeis4.)