%I #17 Oct 02 2017 02:17:26

%S 0,1,3,8,22,58,158,426,1170,3224,8977,25105,70680,199739,566842,

%T 1613454,4605788,13177776,37782903,108522417,312207970,899460505,

%U 2594638480,7493254511,21663019843,62687523055,181561095507,526275453283,1526600618192,4431347014046,12516888508178

%N Number of fixed points over all unlabeled functions on n nodes.

%H N. J. A. Sloane, <a href="/A001372/a001372.gif">Illustration of initial terms of A001372</a>

%F a(n) = Sum_{k=1..n} A217897(n,k)*k.

%t 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}]; cfd=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,2,30}]],1]; CoefficientList[Series[D[Product[1/(1-x^i)^cfd[[i]]/(1-y x^i)^rt[[i]], {i,1,nn-1}],y]/.y->1,{x,0,nn}],x] (* after code given by _Robert A. Russell_ in A000081 *)

%K nonn

%O 0,3

%A _Geoffrey Critzer_, Oct 14 2012