A318864 - OEIS

%I #5 Sep 05 2018 09:05:18

%S 0,1,1,3,8,22,60,167,466,1307,3681,10418,29575,84219,240407,687802,

%T 1971576,5661335,16281377,46888590,135202932,390300559,1127877757,

%U 3262398334,9444747407,27364824226,79344643855,230219356666,668412171376,1941808202980,5644309042885

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

%H Alois P. Heinz, <a href="/A318864/b318864.txt">Table of n, a(n) for n = 7..2137</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))(7):

%p seq(a(n), n=7..37);

%Y Column k=7 of A318758.

%K nonn

%O 7,4

%A _Alois P. Heinz_, Sep 04 2018