A318820 Number of rooted trees with n nodes such that five equals the maximal number of subtrees of the same size extending from the same node.

0, 1, 1, 3, 8, 22, 61, 168, 465, 1302, 3659, 10333, 29255, 83096, 236609, 675311, 1931235, 5532421, 15873557, 45608348, 131208906, 377906025, 1089573851, 3144456980, 9082730826, 26256633715, 75960348880, 219905556560, 637038643771, 1846531053341, 5355395451034

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 A318754.

Programs

Maple

g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
    end:
a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(5):
seq(a(n), n=5..35);