A055334 Number of asymmetric (identity) trees with n nodes and k leaves.

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 3, 3, 0, 0, 0, 4, 8, 3, 0, 0, 5, 14, 10, 0, 0, 0, 7, 25, 29, 6, 0, 0, 8, 40, 65, 25, 1, 0, 0, 10, 62, 135, 90, 13, 0, 0, 12, 89, 252, 244, 69, 1, 0, 0, 14, 127, 445, 591, 276, 27, 0, 0, 16, 173, 739, 1273, 868, 172, 3, 0, 0, 19

Offset: 1

Author

Christian G. Bower, May 12 2000

Keywords

• nonn
• tabf

Comments

A pair of zeros marks the next row.

Examples

			1; 0; 0; 0; 0; 0; 0,0,1; 0,0,1; 0,0,2,1; 0,0,3,3; 0,0,4,8,3; ...
		

Links

• Index entries for sequences related to trees

Crossrefs

Row sums give A000220. Columns 3 through 8: A001399(n-7), A055335-A055339.

Formula

G.f.: A(x, y)=(1-x+x*y)*B(x, y)-(1/2)*(B(x, y)^2+B(x^2, y^2)). B(x, y): g.f. of A055327.