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Search: id:A111169
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| A111169 |
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Number of top simplices in a minimal triangulation of the permutohedron. |
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+0
1
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| 1, 1, 4, 34, 488, 10512, 316224, 12649104, 649094752, 41568338240, 3249938294656, 304670810708736, 33736950933298688, 4356802177994094080, 649031480783423250432, 110477935456564190447616
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The analogous sequence with associahedron in place of permutohedron is (n+1)^{n-1}.
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REFERENCES
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J.-L. Loday, Parking functions and triangulation of the associahedron, ArXiv math:AT/0510380
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LINKS
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J.-L. Loday, More information
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FORMULA
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a(n) = sum_{m=0..n-1} (binom(n+1, m+1) -1) binom(n-1, m) a(m) a(n-m-1). - Robert G. Wilson v (rgwv(at)rgwv.com), Oct 31 2005
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MAPLE
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function y=binom(n, p); y=1; for j = 0 : p-1; y=y*(n-j); end; for j = 1 : p; y=y/j; end; format long; nmax = 14; mm=nmax+1; zp=zeros(mm, 1); zp(1:1) = 1; for n = 1 : nmax; z=0; for p = 0 : n-1; z=z+ (binom(n+1, p+1)-1) * binom(n-1, p) * zp(p+1:p+1) * zp(n-p:n-p); end; zp(n+1:n+1)=z; z; end; n, z
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MATHEMATICA
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f[0] = 1; f[n_] := Sum[(Binomial[n + 1, m + 1] - 1)Binomial[n - 1, m]f[m]f[n - m - 1], {m, 0, n - 1}]; Table[f[n], {n, 0, 16}] (* Robert G. Wilson v *)
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CROSSREFS
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Adjacent sequences: A111166 A111167 A111168 this_sequence A111170 A111171 A111172
Sequence in context: A052629 A151919 A156325 this_sequence A002105 A081972 A134354
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KEYWORD
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easy,nonn
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AUTHOR
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Jean-Louis Loday (loday(AT)math.u-strasbg.fr), Oct 21 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 31 2005
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