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A293510
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Number of connected minimal covers of n vertices.
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20
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1, 1, 1, 4, 23, 241, 3732, 83987, 2666729, 117807298, 7217946453, 612089089261, 71991021616582, 11761139981560581, 2675674695560997301, 849270038176762472316, 376910699272413914514283, 234289022942841270608166061, 204344856617470777364053906796
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OFFSET
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0,4
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COMMENTS
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A cover of a finite set S is a finite set of finite nonempty sets with union S. A cover is minimal if removing any edge results in a cover of strictly fewer vertices. A cover is connected if it is connected as a hypergraph or clutter. Note that minimality is with respect to covering rather than to connectedness (cf. A030019).
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LINKS
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EXAMPLE
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The a(3) = 4 covers are: ((12)(13)), ((12)(23)), ((13)(23)), ((123)).
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MATHEMATICA
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nn=30; ser=Sum[(1+Sum[Binomial[n, i]*StirlingS2[i, k]*(2^k-k-1)^(n-i), {k, 2, n}, {i, k, n}])*x^n/n!, {n, 0, nn}];
Table[n!*SeriesCoefficient[1+Log[ser], {x, 0, n}], {n, 0, nn}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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