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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.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 05 2018
STATUS
approved