A002862 Number of nonisomorphic connected functions with no fixed points, or proper rings with n edges.

0, 1, 2, 5, 11, 31, 77, 214, 576, 1592, 4375, 12183, 33864, 94741, 265461, 746372, 2102692, 5938630, 16803610, 47639902, 135288198, 384812502, 1096141974, 3126648842, 8929715592, 25533447030, 73090099586, 209438176485, 600721031344, 1724585494225

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 41.399.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..750
• R. K. Guy, Letter to N. J. A. Sloane, 1988-04-12 (annotated scanned copy) Includes illustrations for n <= 6.

Crossrefs

(A002861) minus (A000081).

Programs

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}];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 *)

Extensions

More terms and better description from Christian G. Bower