|
%I #17 Oct 02 2017 02:11:55
%S 1,1,2,6,14,38,103,280,773,2160,6053,17064,48320,137260,391091,
%T 1117192,3198217,9173480,26357393,75845591,218550709,630536447,
%U 1821184411,5265514692,15238183779,44136519841,127940010907,371135327740,1077340058523,3129301019091,7015876423459
%N Number of functions on n unlabeled nodes in which all the components are distinct.
%F O.g.f.: Product_{n>=1} (1 + x^n)^A002861(n).
%t Needs["Combinatorica`"];
%t 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 *)
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Oct 13 2012
|
