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A324838
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Number of unlabeled rooted trees with n nodes where the branches of no branch of the root form a submultiset of the branches of the root.
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13
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1, 0, 1, 2, 5, 10, 28, 64, 169, 422, 1108, 2872, 7627, 20202, 54216, 145867, 395288
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OFFSET
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1,4
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LINKS
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EXAMPLE
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The a(1) = 1 through a(6) = 10 rooted trees:
o ((o)) ((oo)) ((ooo)) ((oooo))
(((o))) (((oo))) (((ooo)))
((o)(o)) ((o)(oo))
((o(o))) ((o(oo)))
((((o)))) ((oo(o)))
((((oo))))
(((o)(o)))
(((o(o))))
((o((o))))
(((((o)))))
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MATHEMATICA
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submultQ[cap_, fat_]:=And@@Function[i, Count[fat, i]>=Count[cap, i]]/@Union[List@@cap];
rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];
Table[Length[Select[rtall[n], And@@Table[!submultQ[b, #], {b, #}]&]], {n, 10}]
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CROSSREFS
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Cf. A324694, A324696, A324704, A324738, A324744, A324758, A324759, A324765, A324768, A324771, A324839, A324840, A324844, A324846.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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