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A138650 Table where T(n,k) is the number of unordered trees with n edges (n+1 nodes) whose node out-degrees form the k-th partition of the integer n (in Mathematica order).

%I A138650 #4 May 24 2013 21:38:41
%S A138650 1,1,1,1,1,2,1,1,2,1,4,1,1,2,2,4,4,6,1,1,2,2,4,1,8,7,2,11,9,1,1,2,2,4,
%T A138650 2,8,7,6,5,21,11,9,24,12,1
%N A138650 Table where T(n,k) is the number of unordered trees with n edges (n+1 nodes) whose node out-degrees form the k-th partition of the integer n (in Mathematica order).
%e A138650 For the partition [2,1^2] (a(10)=T(4,4)) there are the four trees:
%e A138650 ..o.....o.....o.....o
%e A138650 ./.\.../.\....|.....|
%e A138650 o...o.o...o...o.....o
%e A138650 |...|.|....../.\....|
%e A138650 o...o.o.....o...o...o
%e A138650 ......|.....|....../.\
%e A138650 ......o.....o.....o...o
%e A138650 Table T(n,k) begins:
%e A138650 1;
%e A138650 1;
%e A138650 1, 1;
%e A138650 1, 2, 1;
%e A138650 1, 2, 1, 4, 1;
%e A138650 1, 2, 2, 4, 4, 6, 1;
%e A138650 1, 2, 2, 4, 1, 8, 7, 2, 11,  9,  1;
%e A138650 1, 2, 2, 4, 2, 8, 7, 6,  5, 21, 11, 9, 24, 12, 1;
%Y A138650 Cf. A000041 (row lengths), A000081 (row sums), A125181.
%K A138650 more,nonn,tabf
%O A138650 0,6
%A A138650 _Franklin T. Adams-Watters_, May 15 2008