A318866 - OEIS

%I #6 Sep 05 2018 08:22:52

%S 0,1,1,3,8,22,60,167,465,1306,3682,10423,29597,84309,240735,688941,

%T 1975403,5673911,16322021,47018394,135613559,391590017,1131902426,

%U 3274897873,9483405008,27483957321,79710659583,231340894684,671840776074,1952268143504,5676161896298

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

%H Alois P. Heinz, <a href="/A318866/b318866.txt">Table of n, a(n) for n = 9..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))(9):

%p seq(a(n), n=9..39);

%Y Column k=9 of A318758.

%K nonn

%O 9,4

%A _Alois P. Heinz_, Sep 04 2018