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A052322
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Number of labeled rooted trees with a forbidden limb of length 3.
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4
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1, 2, 9, 40, 385, 4536, 66409, 1127792, 21981537, 483858640, 11873508361, 321497975448, 9522483900241, 306292854886760, 10632656242583145, 396223803663328096, 15776491521834720961, 668460175137505993248, 30030668624358362706697, 1425868954034374729854920
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OFFSET
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1,2
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COMMENTS
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A rooted tree with a forbidden limb of length k is a rooted tree where the path from any leaf inward hits a branching node or the root within k steps.
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LINKS
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FORMULA
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E.g.f. satisfies A(x) = x*exp(A(x) - x^3).
a(n) ~ sqrt(1+LambertW(-3*exp(-3))) * n^(n-1) * exp(n/3*LambertW(-3*exp(-3))). - Vaclav Kotesovec, Jan 08 2014
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MATHEMATICA
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Rest[CoefficientList[Series[-LambertW[-x*E^(-x^3)], {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Jan 08 2014 *)
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CROSSREFS
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KEYWORD
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nonn,eigen
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AUTHOR
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STATUS
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approved
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