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

10,4

Links

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

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);

Crossrefs

Column k=10 of A318758.

Sequence in context: A318905 A318906 A255705 * A318825 A318866 A318824

Adjacent sequences: A318864 A318865 A318866 * A318868 A318869 A318870

Keyword

nonn

Author

Alois P. Heinz, Sep 04 2018

Status

approved