A318906 Number of n-node rooted trees in which ten 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, 1306, 3681, 10421, 29593, 84298, 240705, 688859, 1975176, 5673279, 16320250, 47013406, 135599456, 391550002, 1131788538, 3274572887, 9482475518, 27481293566, 79703012121, 231318904534, 671777453618, 1952085567096, 5675634863875

Offset

10,3

Links

Alois P. Heinz, Table of n, a(n) for n = 10..2138

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))(10):
seq(a(n), n=10..40);

Crossrefs

Column k=10 of A255704.

Sequence in context: A318903 A318904 A318905 * A255705 A318867 A318825

Adjacent sequences: A318903 A318904 A318905 * A318907 A318908 A318909

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2018

Status

approved