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A217861 Number of functions on n unlabeled nodes in which all the components are distinct. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 13 2012
STATUS
approved

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Last modified June 18 16:37 EDT 2024. Contains 373482 sequences. (Running on oeis4.)