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

1,2

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = Sum_{k=1..n} A127136(n,k)*k.

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 *)

Crossrefs

Sequence in context: A273038 A179905 A034745 * A307073 A143787 A289973

Adjacent sequences: A217857 A217858 A217859 * A217861 A217862 A217863

Keyword

nonn

Author

Geoffrey Critzer, Oct 13 2012

Status

approved