A318901 Number of n-node rooted trees in which five 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, 22, 59, 163, 450, 1254, 3505, 9846, 27740, 78412, 222175, 630993, 1795524, 5118371, 14613211, 41780583, 119605948, 342793785, 983487162, 2824375723, 8118198640, 23353430828, 67230869761, 193682427149, 558333769713, 1610500116245, 4648080322122

Offset

5,3

Links

Alois P. Heinz, Table of n, a(n) for n = 5..2143

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

Crossrefs

Column k=5 of A255704.

Sequence in context: A077848 A300662 A055887 * A278612 A331028 A024581

Adjacent sequences: A318898 A318899 A318900 * A318902 A318903 A318904

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2018

Status

approved