A318900 Number of n-node rooted trees in which four equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.

1, 1, 3, 8, 21, 56, 152, 413, 1131, 3113, 8603, 23861, 66386, 185190, 517807, 1450836, 4072474, 11450141, 32240466, 90901507, 256605905, 725176409, 2051455548, 5808817638, 16462274560, 46691893949, 132531324274, 376443234567, 1069953746735, 3042969864371

Offset: 4

Author

Alois P. Heinz, Sep 05 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..2158

Crossrefs

Column k=4 of A255704.

Programs

Maple

g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
      `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
    end:
a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(4):
seq(a(n), n=4..35);