cp's OEIS Frontend

A255640 Number of n-node rooted trees with a forbidden limb of length 10.

%I A255640 #9 Feb 28 2016 10:51:21
%S A255640 1,1,2,4,9,20,48,115,286,719,1841,4764,12481,32960,87776,235286,
%T A255640 634585,1720432,4686643,12820514,35205696,97009449,268152813,
%U A255640 743354197,2066114863,5756601111,16075024226,44982031393,126114491755,354219140948,996572117396
%N A255640 Number of n-node rooted trees with a forbidden limb of length 10.
%C A255640 Any rootward 10-node path starting at a leaf contains the root or a branching node.
%H A255640 Alois P. Heinz, <a href="/A255640/b255640.txt">Table of n, a(n) for n = 1..1000</a>
%F A255640 a(n) ~ c * d^n / n^(3/2), where d = 2.95571752117840968931298175785458006908910495018670567... and c = 0.43989037737488741580897781267482681067388... . - _Vaclav Kotesovec_, Feb 28 2016
%p A255640 with(numtheory):
%p A255640 g:= proc(n) option remember; `if`(n=0, 1, add(add(d*(g(d-1)-
%p A255640       `if`(d=10, 1, 0)), d=divisors(j))*g(n-j), j=1..n)/n)
%p A255640     end:
%p A255640 a:= n-> g(n-1):
%p A255640 seq(a(n), n=1..40);
%Y A255640 Column k=10 of A255636.
%K A255640 nonn
%O A255640 1,3
%A A255640 _Alois P. Heinz_, Feb 28 2015