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

Author

Alois P. Heinz, Sep 04 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..2138

Crossrefs

Column k=5 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))(5):
seq(a(n), n=5..35);