%I A111169
%S A111169 1,1,4,34,488,10512,316224,12649104,649094752,41568338240,3249938294656,
%T A111169 304670810708736,33736950933298688,4356802177994094080,
%U A111169 649031480783423250432,110477935456564190447616
%N A111169 Number of top simplices in a minimal triangulation of the permutohedron.
%C A111169 The analogous sequence with associahedron in place of permutohedron is 
               (n+1)^{n-1}.
%D A111169 J.-L. Loday, Parking functions and triangulation of the associahedron, 
               ArXiv math:AT/0510380
%H A111169 J.-L. Loday, <a href="http://www-irma.u-strasbg.fr/~loday/">More information</
               a>
%F A111169 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
%p A111169 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
%t A111169 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 *)
%Y A111169 Sequence in context: A052629 A151919 A156325 this_sequence A002105 A081972 
               A158961
%Y A111169 Adjacent sequences: A111166 A111167 A111168 this_sequence A111170 A111171 
               A111172
%K A111169 easy,nonn
%O A111169 0,3
%A A111169 Jean-Louis Loday (loday(AT)math.u-strasbg.fr), Oct 21 2005
%E A111169 More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 31 2005