A217898 Number of fixed points over all unlabeled functions on n nodes.
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
Offset: 0
Keywords
Links
- N. J. A. Sloane, Illustration of initial terms of A001372
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]; 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 *)
Formula
a(n) = Sum_{k=1..n} A217897(n,k)*k.