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

0,6

Links

Table of n, a(n) for n=0..44.

Example

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.

Sequence in context: A305531 A132066 A102190 * A266685 A272620 A304080

Adjacent sequences: A138647 A138648 A138649 * A138651 A138652 A138653

Keyword

more,nonn,tabf

Author

Franklin T. Adams-Watters, May 15 2008

Status

approved