A318862 Number of rooted trees with n nodes such that five equals the maximal number of isomorphic subtrees extending from the same node.

0, 1, 1, 3, 8, 22, 61, 168, 465, 1302, 3659, 10329, 29247, 83076, 236567, 675191, 1930857, 5531409, 15870783, 45600643, 131187583, 377844713, 1089401822, 3143970659, 9081351051, 26252708661, 75949137535, 219873546468, 636947053248, 1846268556446, 5354642063044

Offset

5,4

Links

Alois P. Heinz, Table of n, a(n) for n = 5..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))(5):
seq(a(n), n=5..35);

Crossrefs

Column k=5 of A318758.

Sequence in context: A318821 A014397 A048503 * A318820 A200752 A279378

Adjacent sequences: A318859 A318860 A318861 * A318863 A318864 A318865

Keyword

nonn

Author

Alois P. Heinz, Sep 04 2018

Status

approved