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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 (list; table; graph; refs; listen; history; text; internal format)
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)=(1-x+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(n-4), A055291-A055299.

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

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)