A318867 Number of rooted trees with n nodes such that ten equals the maximal number of isomorphic subtrees extending from the same node.

0, 1, 1, 3, 8, 22, 60, 167, 465, 1306, 3681, 10423, 29598, 84313, 240753, 689013, 1975659, 5674795, 16324964, 47028023, 135644560, 391688786, 1132214211, 3275875432, 9486452173, 27493411246, 79739872605, 231430858159, 672117007940, 1953114145155, 5678747077372

Offset: 10

Author

Alois P. Heinz, Sep 04 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..2139

Crossrefs

Column k=10 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))(10):
seq(a(n), n=10..40);