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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A265846 Number of permutations of {1,2,...,2n} that result in a binary search tree of height n. 4
1, 0, 0, 80, 11360, 1508032, 197163648, 27624399104, 4256968553472, 724948555548672, 136034167652859904, 27976811931437752320, 6269253131872946298880, 1522110257603797873737728, 398311795891656532955725824, 111813044381693547723191418880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

Wikipedia, Binary search tree

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

FORMULA

a(n) = A195581(2n,n) = A244108(2n,n).

a(n) ~ c * d^n * (n-1)!, where d = 19.643259858273023595006139220961408..., c = 0.0646979349409396546649864277836... . - Vaclav Kotesovec, Jan 02 2016

MAPLE

b:= proc(n, k) option remember; `if`(n<2, `if`(k<n, 0, 1),

      add(binomial(n-1, r)*b(r, k-1)*b(n-1-r, k-1), r=0..n-1))

    end:

a:= n-> b(2*n, n)-b(2*n, n-1):

seq(a(n), n=0..20);

MATHEMATICA

b[n_, k_] := b[n, k] = If[n<2, If[k<n, 0, 1], Sum[Binomial[n-1, r]*b[r, k-1]*b[n-1-r, k-1], {r, 0, n-1}]]; a[n_] := b[2*n, n] - b[2*n, n-1]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Feb 25 2017, translated from Maple *)

CROSSREFS

Cf. A195581, A244108.

Sequence in context: A159734 A091754 A118493 * A269145 A187052 A159377

Adjacent sequences:  A265843 A265844 A265845 * A265847 A265848 A265849

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 21 2015

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 October 6 07:09 EDT 2022. Contains 357262 sequences. (Running on oeis4.)