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A318866
Number of rooted trees with n nodes such that nine equals the maximal number of isomorphic subtrees extending from the same node.
2
0, 1, 1, 3, 8, 22, 60, 167, 465, 1306, 3682, 10423, 29597, 84309, 240735, 688941, 1975403, 5673911, 16322021, 47018394, 135613559, 391590017, 1131902426, 3274897873, 9483405008, 27483957321, 79710659583, 231340894684, 671840776074, 1952268143504, 5676161896298
OFFSET
9,4
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))(9):
seq(a(n), n=9..39);
CROSSREFS
Column k=9 of A318758.
Sequence in context: A255705 A318867 A318825 * A318824 A318865 A318823
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 04 2018
STATUS
approved