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A054919
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Number of nonisomorphic connected unlabeled binary relations on n nodes.
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3
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1, 2, 7, 86, 2818, 285382, 96324549, 112087100482, 458071928280897, 6665704296529088252, 349377209492194571020053, 66602723163954144515240479674, 46557323273646194397778583902876038, 120168498151800396724425973133360413846262, 1152049915423012273792614840793828654424980146983
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OFFSET
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0,2
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LINKS
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FORMULA
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Inverse Euler transform of A000595.
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EXAMPLE
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Nonisomorphic connected relations on set {1,2} are {2r1}, {1r1,2r1}, {2r1,2r2}, {1r1,2r1,2r2}, {1r2,2r1}, {1r1,1r2,2r1}, {1r1,1r2,2r1,2r2} so a(2)=7.
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MATHEMATICA
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nn=7; c=Join[{1, 2}, Table[CycleIndex[Join[PairGroup[SymmetricGroup[n], Ordered], Permutations[Range[n^2-n+1, n^2]], 2], s] /. Table[s[i]->2, {i, 1, n^2-n}], {n, 2, nn}]]; f[x_]:=Sum[a[n]x^n, {n, 0, nn}]; b=Sum[c[[n+1]]x^n, {n, 0, nn}]; sol=SolveAlways[b==Normal[Series[Product[1/(1-x^i)^a[i], {i, 1, nn}], {x, 0, nn}]], x]; Table[a[n], {n, 1, nn}]/.sol (* Geoffrey Critzer, Mar 31 2013 *)
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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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EXTENSIONS
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STATUS
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approved
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