A217861 Number of functions on n unlabeled nodes in which all the components are distinct.

1, 1, 2, 6, 14, 38, 103, 280, 773, 2160, 6053, 17064, 48320, 137260, 391091, 1117192, 3198217, 9173480, 26357393, 75845591, 218550709, 630536447, 1821184411, 5265514692, 15238183779, 44136519841, 127940010907, 371135327740, 1077340058523, 3129301019091, 7015876423459

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

O.g.f.: Product_{n>=1} (1 + x^n)^A002861(n).

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]; CoefficientList[Series[Product[(1+ x^i)^c[[i]], {i, 1, nn-1}], {x, 0, nn}], x]  (* after code given by Robert A. Russell in A000081 *)

Crossrefs

Sequence in context: A006654 A127546 A192484 * A188492 A263732 A263733

Adjacent sequences: A217858 A217859 A217860 * A217862 A217863 A217864

Keyword

nonn

Author

Geoffrey Critzer, Oct 13 2012

Status

approved