A318865 Number of rooted trees with n nodes such that eight equals the maximal number of isomorphic subtrees extending from the same node.

0, 1, 1, 3, 8, 22, 60, 167, 465, 1307, 3682, 10422, 29593, 84291, 240663, 688685, 1974519, 5670969, 16312391, 46987389, 135514781, 391278211, 1130924824, 3271850658, 9473951229, 27454745755, 79620703854, 231064697016, 670994912068, 1949683485967, 5668279789793

Offset: 8

Author

Alois P. Heinz, Sep 04 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..2137

Crossrefs

Column k=8 of A318758.

Programs

Maple

h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
      `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
    end:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
    end:
A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
a:= n-> (k-> A(n, k)-A(n, k-1))(8):
seq(a(n), n=8..38);