%I #9 Jun 28 2013 01:24:58

%S 0,1,1,0,3,8,3,0,16,81,32,18,0,125,1024,405,240,160,0,1296,15625,6144,

%T 3645,2560,1875,0,16807,279936,109375,64512,45360,35000,27216,0,

%U 262144,5764801,2239488,1312500,917504,708750,580608,470596,0,4782969

%N Triangular array T(n,k) read by rows, giving number of labeled free trees such that the root is smaller than all its children, with respect to the number n of vertices and to the size k of the subtree rooted at the vertex labeled by 1.

%D C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, Proceedings of FPSAC/SFCA 2000 (Moscow), Springer, pp. 146-157.

%H C. Chauve, S. Dulucq and O. Guibert, <a href="http://www.cecm.sfu.ca/~cchauve/Publications/SFCA00.ps">Enumeration of some labeled trees</a>

%F binomial(n, k-1)*k^(k-2)*(n-k)^(n+1-k)

%p (n,k) -> binomial(n,k-1)*k^(k-2)*(n-k)^(n+1-k);

%o (PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(binomial(n, k-1)*k^(k-2)*(n-k)^(n+1-k), ", ");); print(););} \\ _Michel Marcus_, Jun 27 2013

%Y Cf. A000312.

%K easy,nonn,tabl

%O 1,5

%A Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002