A318866 Number of rooted trees with n nodes such that nine equals the maximal number of isomorphic subtrees extending from the same node.

0, 1, 1, 3, 8, 22, 60, 167, 465, 1306, 3682, 10423, 29597, 84309, 240735, 688941, 1975403, 5673911, 16322021, 47018394, 135613559, 391590017, 1131902426, 3274897873, 9483405008, 27483957321, 79710659583, 231340894684, 671840776074, 1952268143504, 5676161896298

Offset: 9

Author

Alois P. Heinz, Sep 04 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..2138

Crossrefs

Column k=9 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))(9):
seq(a(n), n=9..39);