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A000269
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Number of trees with n nodes, 3 of which are labeled.
(Formerly M3014 N1220)
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9
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3, 16, 67, 251, 888, 3023, 10038, 32722, 105228, 334836, 1056611, 3311784, 10322791, 32026810, 98974177, 304835956, 936147219, 2867586542, 8764280567, 26733395986, 81399821915, 247459136331, 751211286356, 2277496842016
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=3..200
Index entries for sequences related to trees
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FORMULA
| G.f.: A(x) = B(x)^3*(3-2*B(x))/(1-B(x))^3, where B(x) is g.f. for rooted trees with n nodes, cf. A000081. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2001
a(n) = A000524(n)-2*A000243(n).
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CROSSREFS
| Cf. A000055, A000107, A000243, A000444, A000485, A000524-A000526.
Sequence in context: A062960 A044046 A179600 * A015524 A012279 A037098
Adjacent sequences: A000266 A000267 A000268 * A000270 A000271 A000272
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms, new description and formula from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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