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A097172 Total number of brown nodes among tricolored labeled trees on n nodes. 5
3, 4, 185, 1026, 30457, 362664, 10245825, 195060070, 5907674201, 153676400076, 5199628119985, 169205814335754, 6462995557999905, 249877775352089296, 10749867848389013249, 478345428286978038606, 23013713995857481324969 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
LINKS
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)]}.
a(n) ~ (1-2*LambertW(1)^2)*n^(n-1)/(1+LambertW(1)). - Vaclav Kotesovec, Aug 26 2016
MATHEMATICA
Drop[CoefficientList[Series[-LambertW[-x] - LambertW[-LambertW[-x]]- LambertW[-LambertW[-x]]^2, {x, 0, 20}], x] * Range[0, 20]!, 3] (* Vaclav Kotesovec, Aug 26 2016 *)
CROSSREFS
Equals A000169(n)-A097174(n)-A097173(n).
Sequence in context: A041903 A156513 A082213 * A042081 A245456 A042275
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jul 30 2004
STATUS
approved

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Last modified June 16 11:09 EDT 2024. Contains 373429 sequences. (Running on oeis4.)