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A255639
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Number of n-node rooted trees with a forbidden limb of length 9.
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2
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1, 1, 2, 4, 9, 20, 48, 115, 286, 718, 1840, 4761, 12473, 32938, 87716, 235119, 634120, 1719126, 4682962, 12810093, 35176103, 96925151, 267912108, 742665338, 2064139687, 5750927832, 16058703976, 44935017987, 125978892299, 353827590946, 995440328858
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OFFSET
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1,3
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COMMENTS
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Any rootward 9-node path starting at a leaf contains the root or a branching node.
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LINKS
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FORMULA
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a(n) ~ c * d^n / n^(3/2), where d = 2.95562406748808419554567595195333686205085952464972655... and c = 0.439835068532467809288350528155403598039874... . - Vaclav Kotesovec, Feb 28 2016
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MAPLE
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with(numtheory):
g:= proc(n) option remember; `if`(n=0, 1, add(add(d*(g(d-1)-
`if`(d=9, 1, 0)), d=divisors(j))*g(n-j), j=1..n)/n)
end:
a:= n-> g(n-1):
seq(a(n), n=1..40);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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