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

Author

Geoffrey Critzer, Oct 13 2012

Keywords

• nonn

Programs

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.