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A316653
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Number of series-reduced rooted identity trees with n leaves spanning an initial interval of positive integers.
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10
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1, 1, 6, 58, 774, 13171, 272700, 6655962, 187172762, 5959665653, 211947272186, 8327259067439, 358211528524432, 16744766791743136, 845195057333580332, 45814333121920927067, 2654330505021077873594, 163687811930206581162063, 10705203621191765328300832
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OFFSET
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1,3
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COMMENTS
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A rooted tree is series-reduced if every non-leaf node has at least two branches. It is an identity tree if no branch appears multiple times under the same root.
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LINKS
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EXAMPLE
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The a(3) = 6 trees are (1(12)), (2(12)), (1(23)), (2(13)), (3(12)), (123).
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MATHEMATICA
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sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
gro[m_]:=If[Length[m]==1, m, Select[Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m], Length[#]>1&])], UnsameQ@@#&]];
allnorm[n_Integer]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];
Table[Sum[Length[gro[m]], {m, allnorm[n]}], {n, 5}]
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PROG
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WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
R(n, k)={my(v=[k]); for(n=2, n, v=concat(v, WeighT(concat(v, [0]))[n])); v}
seq(n)={sum(k=1, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) )} \\ Andrew Howroyd, Sep 14 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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