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A071211 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. 0

%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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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)