login
A318900
Number of n-node rooted trees in which four 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, 21, 56, 152, 413, 1131, 3113, 8603, 23861, 66386, 185190, 517807, 1450836, 4072474, 11450141, 32240466, 90901507, 256605905, 725176409, 2051455548, 5808817638, 16462274560, 46691893949, 132531324274, 376443234567, 1069953746735, 3042969864371
OFFSET
4,3
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))(4):
seq(a(n), n=4..35);
CROSSREFS
Column k=4 of A255704.
Sequence in context: A090413 A128105 A085560 * A243633 A094374 A008909
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 05 2018
STATUS
approved