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A217898
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Number of fixed points over all unlabeled functions on n nodes.
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0
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0, 1, 3, 8, 22, 58, 158, 426, 1170, 3224, 8977, 25105, 70680, 199739, 566842, 1613454, 4605788, 13177776, 37782903, 108522417, 312207970, 899460505, 2594638480, 7493254511, 21663019843, 62687523055, 181561095507, 526275453283, 1526600618192, 4431347014046, 12516888508178
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} A217897(n,k)*k.
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MATHEMATICA
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Needs["Combinatorica`"]; nn=30; s[n_, k_]:=s[n, k]=a[n+1-k]+If[n<2 k, 0, s[n-k, k]]; a[1]=1; a[n_]:=a[n]=Sum[a[i] s[n-1, i] i, {i, 1, n-1}]/(n-1); rt=Table[a[i], {i, 1, nn}]; cfd=Drop[Apply[Plus, Table[Take[CoefficientList[CycleIndex[CyclicGroup[n], s]/.Table[s[j]->Table[Sum[rt[[i]] x^(k*i), {i, 1, nn}], {k, 1, nn}][[j]], {j, 1, nn}], x], nn], {n, 2, 30}]], 1]; CoefficientList[Series[D[Product[1/(1-x^i)^cfd[[i]]/(1-y x^i)^rt[[i]], {i, 1, nn-1}], y]/.y->1, {x, 0, nn}], x] (* after code given by Robert A. Russell in A000081 *)
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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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