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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

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

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)