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A300626
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Number of inequivalent colorings of free pure symmetric multifunctions (with empty expressions allowed) with n positions.
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6
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1, 1, 3, 11, 43, 187, 872, 4375, 23258, 130485, 767348, 4710715, 30070205, 198983975, 1361361925, 9607908808, 69812787049, 521377973359, 3996036977270, 31389624598631, 252408597286705, 2075472033455894, 17434190966525003, 149476993511444023, 1307022313790487959
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OFFSET
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0,3
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COMMENTS
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A free pure symmetric multifunction (with empty expressions allowed) f in EOME is either (case 1) a positive integer, or (case 2) a possibly empty expression of the form h[g_1, ..., g_k] where k >= 0, h is in EOME, each of the g_i for i = 1, ..., k is in EOME, and for i < j we have g_i <= g_j under a canonical total ordering of EOME, such as the Mathematica ordering of expressions.
Also the number of inequivalent colorings of orderless Mathematica expressions with n positions.
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LINKS
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EXAMPLE
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Inequivalent representatives of the a(3) = 11 colorings:
1[1,1] 1[2,2] 1[1,2] 1[2,3]
1[1[]] 1[2[]]
1[][1] 1[][2]
1[1][] 1[2][]
1[][][]
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PROG
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(PARI) \\ See links in A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(p=O(x)); for(n=1, n, p = x*sv(1) + x*p*sExp(p)); p}
InequivalentColoringsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 30 2020
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CROSSREFS
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Cf. A000612, A007716, A052893, A053492, A277996, A279944, A280000, A317652, A317655, A317656, A317676.
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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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