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A244709
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Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 8.
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2
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1, 1, 3, 6, 15, 31, 74, 159, 365, 803, 1813, 4022, 9038, 20128, 45093, 100656, 225263, 503320, 1126045, 2517487, 5631913, 12596046, 28181168, 63045684, 141071758, 315668674, 706452161, 1581088178, 3538954508, 7921759060, 17733983146, 39702719910, 88893039358
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OFFSET
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9,3
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COMMENTS
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In a rooted tree with thinning limbs the outdegree of a parent node is larger than or equal to the outdegree of any of its child nodes.
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LINKS
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MAPLE
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b:= proc(n, i, h, v) option remember; `if`(n=0,
`if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
`if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)
*b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
end:
A:= proc(n, k) option remember;
`if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
end:
a:= n-> b(n-1$2, 8$2):
seq(a(n), n=9..50);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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