A151880 Triangle: R*(n,k) (n>=2, k from 2 to n-1 or to 2 if n = 2), where R*(n,k) = number of trees with n nodes and k unlabeled end-nodes.

1, 1, 1, 1, 1, 2, 3, 1, 3, 9, 12, 1, 4, 18, 52, 60, 1, 5, 30, 136, 360, 360

Offset

0,6

Comments

All nodes are labeled except for the end-nodes.

Links

Table of n, a(n) for n=0..21.

F. Harary, A. Mowshowitz and J. Riordan, Labeled trees with unlabeled end-points, J. Combin. Theory, 6 (1969), 60-64.

Formula

There is an explicit formula in terms of Stirling numbers of the second kind.

Example

Triangle (in fact the columns in the original have been reversed and the triangle transposed):
(n=2) 1
(n=3) 1
(n=4) 1 1
(n=5) 1 2 3
(n=6) 1 3 9 12
(n=7) 1 4 18 52 60
(n=8) 1 5 30 136 360 360

Crossrefs

See A213262 for a better version with more terms and a program.

Row sums give A001258.

Sequence in context: A111589 A259760 A010027 * A108990 A145080 A065078

Adjacent sequences: A151877 A151878 A151879 * A151881 A151882 A151883

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jul 21 2009

Status

approved