A318899 Number of n-node rooted trees in which three 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, 7, 18, 45, 116, 298, 776, 2025, 5322, 14030, 37155, 98685, 262961, 702497, 1881475, 5050140, 13583622, 36605565, 98821445, 267220361, 723704046, 1962830775, 5330900916, 14497096134, 39472561082, 107601053713, 293643574776, 802203904616, 2193758306687

Offset: 3

Author

Alois P. Heinz, Sep 05 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..2209

Crossrefs

Column k=3 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))(3):
seq(a(n), n=3..35);