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A318231
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Number of inequivalent leaf-colorings of series-reduced rooted trees with n nodes.
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12
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1, 0, 2, 3, 9, 23, 73, 229, 796, 2891, 11118, 44695, 187825, 820320, 3716501, 17413308, 84209071, 419461933, 2148673503, 11301526295, 60956491070, 336744177291, 1903317319015, 10995856040076, 64873456288903, 390544727861462, 2397255454976268, 14993279955728851
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OFFSET
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1,3
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COMMENTS
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In a series-reduced rooted tree, every non-leaf node has at least two branches.
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LINKS
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EXAMPLE
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Inequivalent representatives of the a(6) = 23 leaf-colorings:
(11(11)) (1(111)) (11111)
(11(12)) (1(112)) (11112)
(11(22)) (1(122)) (11122)
(11(23)) (1(123)) (11123)
(12(11)) (1(222)) (11223)
(12(12)) (1(223)) (11234)
(12(13)) (1(234)) (12345)
(12(33))
(12(34))
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PROG
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(PARI) \\ See links in A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(v=vector(n)); v[1]=sv(1); for(n=2, #v, v[n] = polcoef( sEulerT(x*Ser(concat(v[1..n-2], [0]))), n-1 )); x*Ser(v)}
InequivalentColoringsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 11 2020
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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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