A217896 Number of unlabeled functions on n nodes that have at least one fixed point.
0, 1, 2, 5, 13, 34, 90, 243, 660, 1818, 5045, 14102, 39639, 111982, 317533, 903464, 2577724, 7372542, 21130127, 60672017, 174492633, 502568607, 1449360241, 4184719174, 12095325486, 34993693260, 101332159421, 293669741860, 851722291650, 2471948910379, 6824540110584
Offset: 0
Keywords
Programs
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Mathematica
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];cf=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,1,30}]],1];fd=CoefficientList[Series[Product[1/(1-x^i)^cfd[[i]],{i,1,nn-1}],{x,0,nn}],x];f=CoefficientList[Series[Product[1/(1-x^i)^cf[[i]],{i,1,nn-1}],{x,0,nn}],x];f-fd (* Geoffrey Critzer, Oct 14 2012, after code given by Robert A. Russell in A000081 *)
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