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A318860
Number of rooted trees with n nodes such that three equals the maximal number of isomorphic subtrees extending from the same node.
2
0, 1, 1, 3, 9, 23, 60, 164, 443, 1209, 3319, 9150, 25326, 70335, 195870, 546823, 1529935, 4288662, 12042447, 33866604, 95373852, 268925258, 759157224, 2145298117, 6068251826, 17180172176, 48680092670, 138041661905, 391725281701, 1112360700816, 3160707529077
OFFSET
3,4
LINKS
MAPLE
h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
`if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
end:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
end:
A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
a:= n-> (k-> A(n, k)-A(n, k-1))(3):
seq(a(n), n=3..33);
CROSSREFS
Column k=3 of A318758.
Sequence in context: A309301 A323798 A180488 * A318818 A026599 A061647
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 04 2018
STATUS
approved