%I M1403 N0547 #35 Oct 02 2017 02:14:09

%S 0,1,2,5,11,31,77,214,576,1592,4375,12183,33864,94741,265461,746372,

%T 2102692,5938630,16803610,47639902,135288198,384812502,1096141974,

%U 3126648842,8929715592,25533447030,73090099586,209438176485,600721031344,1724585494225

%N Number of nonisomorphic connected functions with no fixed points, or proper rings with n edges.

%D R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 41.399.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A002862/b002862.txt">Table of n, a(n) for n = 1..750</a>

%H R. K. Guy, <a href="/A000081/a000081.pdf">Letter to N. J. A. Sloane, 1988-04-12</a> (annotated scanned copy) Includes illustrations for n <= 6.

%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] (* _Geoffrey Critzer_, Oct 14 2012, after code given by _Robert A. Russell_ in A000081 *)

%Y (A002861) minus (A000081).

%K nonn,nice

%O 1,3

%A _N. J. A. Sloane_

%E More terms and better description from _Christian G. Bower_