

A055290


Triangle of trees with n nodes and k leaves, 2 <= k <= n.


17



1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 1, 3, 4, 2, 1, 0, 1, 4, 8, 6, 3, 1, 0, 1, 5, 14, 14, 9, 3, 1, 0, 1, 7, 23, 32, 26, 12, 4, 1, 0, 1, 8, 36, 64, 66, 39, 16, 4, 1, 0, 1, 10, 54, 123, 158, 119, 60, 20, 5, 1, 0, 1, 12, 78, 219, 350, 325, 202, 83, 25, 5, 1, 0, 1, 14, 110, 377, 727
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OFFSET

2,12


REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 80, Problem 3.9.


LINKS

Table of n, a(n) for n=2..84.
Index entries for sequences related to trees


FORMULA

G.f.: A(x, y)=(1x+x*y)*B(x, y)+(1/2)*(B(x^2, y^2)B(x, y)^2), where B(x, y) is g.f. of A055277.


EXAMPLE

Triangle starts with
n=2: 1;
n=3: 1,0;
n=4: 1,1,0;
n=5: 1,1,1,0;
n=6: 1,2,2,1,0;
...


CROSSREFS

Row sums give A000055, row sums with weight k give A003228.
Columns 3 through 12: A001399(n4), A055291A055299.
Cf. A055300, A055301.
Sequence in context: A037836 A194522 A165013 * A125629 A141335 A133624
Adjacent sequences: A055287 A055288 A055289 * A055291 A055292 A055293


KEYWORD

nonn,tabl


AUTHOR

Christian G. Bower, May 09 2000


STATUS

approved



