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A292214
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Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than eight.
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2
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0, 1, 1, 2, 5, 12, 33, 90, 261, 765, 2309, 7058, 21932, 68843, 218378, 698268, 2249370, 7291072, 23766308, 77850244, 256141505, 846090860, 2804864997, 9328658392, 31118365152, 104086821258, 349029100890, 1173087112579, 3951183698640, 13334782347941
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OFFSET
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0,4
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LINKS
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MAPLE
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b:= proc(n, i, v) 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)+j-1, j)*
b(n-i*j, i-1, v-j), j=0..min(n/i, v)))))
end:
a:= proc(n) option remember; `if`(n<2, n,
add(b(n, n+1-j, j), j=2..min(n, 8)))
end:
seq(a(n), n=0..35);
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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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