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).

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, 2, 8, 7, 6, 5, 21, 11, 9, 24, 12, 1

Offset: 0

Author

Franklin T. Adams-Watters, May 15 2008

Keywords

• more
• nonn
• tabf

Examples

			For the partition [2,1^2] (a(10)=T(4,4)) there are the four trees:
..o.....o.....o.....o
./.\.../.\....|.....|
o...o.o...o...o.....o
|...|.|....../.\....|
o...o.o.....o...o...o
......|.....|....../.\
......o.....o.....o...o
Table T(n,k) begins:
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, 2, 8, 7, 6,  5, 21, 11, 9, 24, 12, 1;
		

Crossrefs

Cf. A000041 (row lengths), A000081 (row sums), A125181.