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A111169 Number of top simplices in a minimal triangulation of the permutohedron. 1
1, 1, 4, 34, 488, 10512, 316224, 12649104, 649094752, 41568338240, 3249938294656, 304670810708736, 33736950933298688, 4356802177994094080, 649031480783423250432, 110477935456564190447616, 21310050396755400705088512, 4623833701942527407032074240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The analogous sequence with associahedron in place of permutohedron is (n+1)^{n-1}.

This also counts maximal chains in the shard intersection orders of type A, see Theorem 1.3 in Reading reference. - F. Chapoton, Apr 29 2015

LINKS

M. F. Hasler, Table of n, a(n) for n = 0..100

J.-L. Loday, More information

J.-L. Loday, Parking functions and triangulation of the associahedron, ArXiv math:AT/0510380

N. Reading, Noncrossing partitions and the shard intersection order, arXiv:0909.3288 [math.CO], 2009.

N. Reading, Noncrossing partitions and the shard intersection order, J. Algebraic Combin. 33 (2011), no. 4.

FORMULA

a(n) = Sum_{m=0..n-1} (binomial(n+1, m+1) -1) binomial(n-1, m) a(m) a(n-m-1). - Robert G. Wilson v, Oct 31 2005

MAPLE

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

MATHEMATICA

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, Oct 31 2005 *)

PROG

(PARI) a111169=[1]; A111169(n)={n<3&&return(n^n); global(a111169); while(n>m=#a111169, a111169=concat(a111169, sum(k=1, m-1, (binomial(m+2, k+1)-1)*binomial(m, k)*a111169[k]*a111169[m-k], 2*(m+1)*a111169[m]))); a111169[n]} \\ M. F. Hasler, May 02 2015

CROSSREFS

Sequence in context: A198976 A156325 A248654 * A274244 A002105 A198717

Adjacent sequences:  A111166 A111167 A111168 * A111170 A111171 A111172

KEYWORD

easy,nonn

AUTHOR

Jean-Louis Loday (loday(AT)math.u-strasbg.fr), Oct 21 2005

EXTENSIONS

More terms from Robert G. Wilson v, Oct 31 2005

STATUS

approved

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Last modified May 23 21:10 EDT 2018. Contains 304483 sequences. (Running on oeis4.)