A002862 Number of nonisomorphic connected functions with no fixed points, or proper rings with n edges. (Formerly M1403 N0547)

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

1,3

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.

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 *)

Crossrefs

(A002861) minus (A000081).

Sequence in context: A291139 A139467 A124481 * A190865 A275427 A139464

Adjacent sequences: A002859 A002860 A002861 * A002863 A002864 A002865

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms and better description from Christian G. Bower

Status

approved