cp's OEIS Frontend

A071210 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 degree k of the root.

%I A071210 #10 Jun 27 2013 10:22:03
%S A071210 1,3,1,18,8,1,160,80,15,1,1875,1000,225,24,1,27216,15120,3780,504,35,
%T A071210 1,470596,268912,72030,10976,980,48,1,9437184,5505024,1548288,258048,
%U A071210 26880,1728,63,1,215233605,127545840,37200870,6613488,765450,58320
%N A071210 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 degree k of the root.
%H A071210 C. Chauve, S. Dulucq and O. Guibert, <a href="http://www.cecm.sfu.ca/~cchauve/Publications/SFCA00.ps">Enumeration of some labeled trees</a>, Proceedings of FPSAC/SFCA 2000 (Moscow), Springer, pp. 146-157.
%F A071210 T(n,k) = binomial(n+1, k+1)*k*n^(n-k-1).
%p A071210 (n,k) -> binomial(n+1,k+1)*k*n^(n-k-1)
%o A071210 (PARI) tabl(nn) = for (n=1, nn, for (k=1, n, print1(binomial(n+1, k+1)*k*n^(n-k-1), ", ");); print) \\ _Michel Marcus_, Jun 27 2013
%Y A071210 Cf. A000312, A052182 (first column).
%K A071210 easy,nonn,tabl
%O A071210 1,2
%A A071210 Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002