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A292235
Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals nine.
2
1, 2, 7, 23, 78, 262, 893, 3040, 10410, 35718, 122918, 423861, 1464642, 5069475, 17574187, 61007028, 212044176, 737835578, 2570028204, 8960286527, 31266462620, 109188954531, 381589000393, 1334464142298, 4669723965497, 16350466246944, 57280522330579
OFFSET
9,2
MAPLE
b:= proc(n, i, v, k) option remember; `if`(n=0,
`if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
`if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
end:
A:= proc(n, k) option remember; `if`(n<2, n,
add(b(n, n+1-j, j, k), j=2..min(n, k)))
end:
a:= n-> A(n, 9)-A(n, 8):
seq(a(n), n=9..40);
CROSSREFS
Column k=9 of A292086.
Sequence in context: A292232 A292233 A292234 * A292236 A292087 A091702
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 12 2017
STATUS
approved