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A292234
Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals eight.
2
1, 2, 7, 23, 78, 262, 893, 3039, 10405, 35692, 122807, 423392, 1462748, 5061942, 17544791, 60893535, 211610421, 736189821, 2563823467, 8937012397, 31179543205, 108865543805, 380389514123, 1330027798273, 4653356214277, 16290208735442, 57059113819218
OFFSET
8,2
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, 8)-A(n, 7):
seq(a(n), n=8..35);
CROSSREFS
Column k=8 of A292086.
Sequence in context: A292231 A292232 A292233 * A292235 A292236 A292087
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 12 2017
STATUS
approved