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%I A255639 #9 Feb 28 2016 10:48:56
%S A255639 1,1,2,4,9,20,48,115,286,718,1840,4761,12473,32938,87716,235119,
%T A255639 634120,1719126,4682962,12810093,35176103,96925151,267912108,
%U A255639 742665338,2064139687,5750927832,16058703976,44935017987,125978892299,353827590946,995440328858
%N A255639 Number of n-node rooted trees with a forbidden limb of length 9.
%C A255639 Any rootward 9-node path starting at a leaf contains the root or a branching node.
%H A255639 Alois P. Heinz, <a href="/A255639/b255639.txt">Table of n, a(n) for n = 1..1000</a>
%F A255639 a(n) ~ c * d^n / n^(3/2), where d = 2.95562406748808419554567595195333686205085952464972655... and c = 0.439835068532467809288350528155403598039874... . - _Vaclav Kotesovec_, Feb 28 2016
%p A255639 with(numtheory):
%p A255639 g:= proc(n) option remember; `if`(n=0, 1, add(add(d*(g(d-1)-
%p A255639       `if`(d=9, 1, 0)), d=divisors(j))*g(n-j), j=1..n)/n)
%p A255639     end:
%p A255639 a:= n-> g(n-1):
%p A255639 seq(a(n), n=1..40);
%Y A255639 Column k=9 of A255636.
%K A255639 nonn
%O A255639 1,3
%A A255639 _Alois P. Heinz_, Feb 28 2015

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