A318904 Number of n-node rooted trees in which eight 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, 60, 167, 465, 1305, 3677, 10407, 29545, 84137, 240180, 687169, 1969805, 5656352, 16267296, 46848655, 135089324, 389976522, 1126951399, 3259744738, 9437132452, 27342937037, 79281644947, 230037790501, 667888276997, 1940294941620, 5639933760363

Offset

8,3

Links

Alois P. Heinz, Table of n, a(n) for n = 8..2137

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))(8):
seq(a(n), n=8..38);

Crossrefs

Column k=8 of A255704.

Sequence in context: A155020 A318902 A318903 * A318905 A318906 A255705

Adjacent sequences: A318901 A318902 A318903 * A318905 A318906 A318907

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2018

Status

approved