A318862 - OEIS

%I #5 Sep 05 2018 09:50:02

%S 0,1,1,3,8,22,61,168,465,1302,3659,10329,29247,83076,236567,675191,

%T 1930857,5531409,15870783,45600643,131187583,377844713,1089401822,

%U 3143970659,9081351051,26252708661,75949137535,219873546468,636947053248,1846268556446,5354642063044

%N Number of rooted trees with n nodes such that five equals the maximal number of isomorphic subtrees extending from the same node.

%H Alois P. Heinz, <a href="/A318862/b318862.txt">Table of n, a(n) for n = 5..2138</a>

%p h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),

%p       `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))

%p     end:

%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))

%p     end:

%p A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):

%p a:= n-> (k-> A(n, k)-A(n, k-1))(5):

%p seq(a(n), n=5..35);

%Y Column k=5 of A318758.

%K nonn

%O 5,4

%A _Alois P. Heinz_, Sep 04 2018