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A318901
Number of n-node rooted trees in which five 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, 59, 163, 450, 1254, 3505, 9846, 27740, 78412, 222175, 630993, 1795524, 5118371, 14613211, 41780583, 119605948, 342793785, 983487162, 2824375723, 8118198640, 23353430828, 67230869761, 193682427149, 558333769713, 1610500116245, 4648080322122
OFFSET
5,3
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))(5):
seq(a(n), n=5..35);
CROSSREFS
Column k=5 of A255704.
Sequence in context: A077848 A300662 A055887 * A278612 A331028 A024581
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 05 2018
STATUS
approved