cp's OEIS Frontend

A071209 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.

%I A071209 #9 Jun 28 2013 01:24:58
%S A071209 0,1,1,0,3,8,3,0,16,81,32,18,0,125,1024,405,240,160,0,1296,15625,6144,
%T A071209 3645,2560,1875,0,16807,279936,109375,64512,45360,35000,27216,0,
%U A071209 262144,5764801,2239488,1312500,917504,708750,580608,470596,0,4782969
%N A071209 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 A071209 C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, Proceedings of FPSAC/SFCA 2000 (Moscow), Springer, pp. 146-157.
%H A071209 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 A071209 binomial(n, k-1)*k^(k-2)*(n-k)^(n+1-k)
%p A071209 (n,k) -> binomial(n,k-1)*k^(k-2)*(n-k)^(n+1-k);
%o A071209 (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 A071209 Cf. A000312.
%K A071209 easy,nonn,tabl
%O A071209 1,5
%A A071209 Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002