cp's OEIS Frontend

A255638 Number of n-node rooted trees with a forbidden limb of length 8.

%I A255638 #11 Feb 28 2016 10:46:18
%S A255638 1,1,2,4,9,20,48,115,285,717,1837,4753,12451,32878,87549,234654,
%T A255638 632814,1715446,4672544,12780511,35091842,96684570,267223650,
%U A255638 740691451,2058470490,5734620428,16011730686,44799543203,125587727914,352696990890,992169406959
%N A255638 Number of n-node rooted trees with a forbidden limb of length 8.
%C A255638 Any rootward 8-node path starting at a leaf contains the root or a branching node.
%H A255638 Alois P. Heinz, <a href="/A255638/b255638.txt">Table of n, a(n) for n = 1..1000</a>
%F A255638 a(n) ~ c * d^n / n^(3/2), where d = 2.95534758805897943282870965508636011438518881375... and c = 0.43969195292137654501555629074396535899093... . - _Vaclav Kotesovec_, Feb 28 2016
%p A255638 with(numtheory):
%p A255638 g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
%p A255638       `if`(d=k, 1, 0)), d=divisors(j))*g(n-j, k), j=1..n)/n)
%p A255638     end:
%p A255638 a:= n-> g(n-1, 8):
%p A255638 seq(a(n), n=1..40);
%Y A255638 Column k=8 of A255636.
%K A255638 nonn
%O A255638 1,3
%A A255638 _Alois P. Heinz_, Feb 28 2015