%I #7 Jun 27 2013 08:07:23
%S 1,3,1,16,8,3,125,75,40,16,1296,864,540,300,125,16807,12005,8232,5292,
%T 3024,1296,262144,196608,143360,100352,65856,38416,16807,4782969,
%U 3720087,2834352,2099520,1492992,995328,589824,262144,100000000
%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 label k of the root.
%D C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, Proceedings of FPSAC/SFCA 2000 (Moscow), Springer, pp. 146-157.
%F T(n,k) = (n-k)*(n+1)^(n-k-1)*n^(k-1).
%p T:= (n, k)-> (n-k)*(n+1)^(n-k-1)*n^(k-1):
%p seq(seq(T(n, k), k=0..n-1), n=1..10);
%o (PARI) tabl(nn) = {for (n=1, nn, for (k=0, n-1, print1((n-k)*(n+1)^(n-k-1)*n^(k-1), ", ");); print(););} \\ _Michel Marcus_, Jun 27 2013
%Y Cf. A000312, A000272 (first column).
%K easy,nonn,tabl
%O 1,2
%A Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002
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