A217860 Number of components over all functions on n unlabeled nodes.
1, 4, 11, 33, 88, 254, 697, 1984, 5585, 15938, 45424, 130381, 374450, 1079361, 3115291, 9010177, 26090857, 75656608, 219603868, 638075127, 1855506355, 5399995044, 15726096741, 45827313178, 133621409595, 389814176004, 1137757623214, 3322288247568, 9705228070231, 26283373417131
Offset: 1
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}];c=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];Drop[CoefficientList[Series[D[Product[1/(1-y x^i)^c[[i]],{i,1,nn-1}],y]/.y->1,{x,0,nn}],x],1] (* after code given by Robert A. Russell in A000081 *)
Formula
a(n) = Sum_{k=1..n} A127136(n,k)*k.