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A055290
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Triangle of trees with n nodes and k leaves.
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12
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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; internal format)
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OFFSET
| 2,12
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REFERENCES
| F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 80, Problem 3.9.
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LINKS
| Index entries for sequences related to trees
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FORMULA
| G.f.: A(x, y)=(1-x+x*y)*B(x, y)+(1/2)*(B(x^2, y^2)-B(x, y)^2). B(x, y): g.f. of A055277.
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EXAMPLE
| 1; 1,0; 1,1,0; 1,1,1,0; 1,2,2,1,0; ...
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CROSSREFS
| Row sums give A000055. 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
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KEYWORD
| nonn,tabl
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), May 09 2000
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