A265846 Number of permutations of {1,2,...,2n} that result in a binary search tree of height n.

1, 0, 0, 80, 11360, 1508032, 197163648, 27624399104, 4256968553472, 724948555548672, 136034167652859904, 27976811931437752320, 6269253131872946298880, 1522110257603797873737728, 398311795891656532955725824, 111813044381693547723191418880

Offset: 0

Author

Alois P. Heinz, Dec 21 2015

Keywords

• nonn

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

Crossrefs

Cf. A195581, A244108.

Programs

Maple

b:= proc(n, k) option remember; `if`(n<2, `if`(k 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[kJean-François Alcover, Feb 25 2017, translated from Maple *)

Formula

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

a(n) ~ c * d^n * (n-1)!, where d = -16*LambertW(-1, -exp(-1/2)/2)^2 / (1 + 2*LambertW(-1, -exp(-1/2)/2)) = 19.643259858273023595006139220961408..., c = 1/(2^(5/2)*Pi*sqrt(-1 - LambertW(-1, -exp(-1/2)/2))) = 0.0646979349409396546649864277836... . - Vaclav Kotesovec, Jan 02 2016, updated Mar 17 2024 and May 14 2025