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A097172
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Total number of brown nodes among tricolored labeled trees on n nodes.
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4
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3, 4, 185, 1026, 30457, 362664, 10245825, 195060070, 5907674201, 153676400076, 5199628119985, 169205814335754, 6462995557999905, 249877775352089296, 10749867848389013249, 478345428286978038606, 23013713995857481324969
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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LINKS
| S. Coulomb and M. Bauer, On vertex covers, matchings and random trees
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FORMULA
| E.g.f.: A(x) = T(x)+T(-T(x))-T(-T(x))^2, with T(x)=Sum[k=1..inf, A000169(k)/k!*x^k].
a(n) = -n^(n-1) * {1 + Sum[l=1..n, (-l/n)^l*(2/l-1)*C(n, l)]}.
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CROSSREFS
| Equals A000169(n)-A097174(n)-A097173(n).
Cf. A097170, A097171, A097173, A097174, A000272.
Sequence in context: A041903 A156513 A082213 * A042081 A042275 A012861
Adjacent sequences: A097169 A097170 A097171 * A097173 A097174 A097175
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, Jul 30 2004
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