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A054919
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Number of nonisomorphic connected unlabeled binary relations on n nodes.
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1
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2, 7, 86, 2818, 285382, 96324549, 112087100482, 458071928280897, 6665704296529088252, 349377209492194571020053, 66602723163954144515240479674, 46557323273646194397778583902876038
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..12.
V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
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FORMULA
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EULERi 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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Sequence in context: A163855 A041291 A209331 * A119157 A079701 A096208
Adjacent sequences: A054916 A054917 A054918 * A054920 A054921 A054922
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, May 24 2000
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EXTENSIONS
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More terms from Vladeta Jovovic, Jul 16 2000
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STATUS
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approved
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