A318903 Number of n-node rooted trees in which seven 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, 464, 1302, 3666, 10370, 29421, 83736, 238891, 683088, 1956968, 5616281, 16142818, 46463814, 133903792, 386336345, 1115804329, 3225691950, 9333321576, 27027053245, 78322024353, 227126864470, 659069928758, 1913612752613, 5559288014180

Offset

7,3

Links

Alois P. Heinz, Table of n, a(n) for n = 7..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))(7):
seq(a(n), n=7..37);

Crossrefs

Column k=7 of A255704.

Sequence in context: A028859 A155020 A318902 * A318904 A318905 A318906

Adjacent sequences: A318900 A318901 A318902 * A318904 A318905 A318906

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2018

Status

approved