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A265846
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Number of permutations of {1,2,...,2n} that result in a binary search tree of height n.
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4
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1, 0, 0, 80, 11360, 1508032, 197163648, 27624399104, 4256968553472, 724948555548672, 136034167652859904, 27976811931437752320, 6269253131872946298880, 1522110257603797873737728, 398311795891656532955725824, 111813044381693547723191418880
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OFFSET
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0,4
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LINKS
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FORMULA
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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 = 0.0646979349409396546649864277836... . - Vaclav Kotesovec, Jan 02 2016, updated Mar 17 2024
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MAPLE
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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);
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MATHEMATICA
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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-François Alcover, Feb 25 2017, translated from Maple *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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