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

9,4

Links

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

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);

Crossrefs

Column k=9 of A318758.

Sequence in context: A255705 A318867 A318825 * A318824 A318865 A318823

Adjacent sequences: A318863 A318864 A318865 * A318867 A318868 A318869

Keyword

nonn

Author

Alois P. Heinz, Sep 04 2018

Status

approved