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A301871
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Number of N- and bowtie-free posets with n elements.
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2
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1, 2, 5, 14, 40, 121, 373, 1184, 3823, 12554, 41733, 140301, 475934, 1627440, 5602983, 19406703, 67574371, 236409625, 830582851, 2929246932, 10366380583, 36801225872, 131021870786, 467701875135, 1673584553886, 6002046468815, 21570135722058, 77668429499325, 280167079428684, 1012323004985313
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OFFSET
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1,2
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COMMENTS
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The number of n-element posets that do not include the two 4-element posets "N" and "bowtie" as induced subposets.
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LINKS
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FORMULA
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G.f. V(x) = 1 + x + 2x + 5x^2 + ... satisfies V(x) = (1-x)exp[sum_{m >=1} (2x^m-x^(2m))V(x^m)/m] (see Razanajatovo Misanantenaina/Wagner).
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MATHEMATICA
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V=1; Do[V = Normal[Series[(1 - x) Exp[Sum[(2 x^m - x^(2 m)) (V /. x -> x^m)/m, {m, 1, n}]], {x, 0, n}]], {n, 1, 20}]; Table[Coefficient[V, x, n], {n, 1, 20}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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