A217896 Number of unlabeled functions on n nodes that have at least one fixed point.

0, 1, 2, 5, 13, 34, 90, 243, 660, 1818, 5045, 14102, 39639, 111982, 317533, 903464, 2577724, 7372542, 21130127, 60672017, 174492633, 502568607, 1449360241, 4184719174, 12095325486, 34993693260, 101332159421, 293669741860, 851722291650, 2471948910379, 6824540110584

Offset

0,3

Comments

See A001372 and A001373

Links

Table of n, a(n) for n=0..30.

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]; cf=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]; fd=CoefficientList[Series[Product[1/(1-x^i)^cfd[[i]], {i, 1, nn-1}], {x, 0, nn}], x]; f=CoefficientList[Series[Product[1/(1-x^i)^cf[[i]], {i, 1, nn-1}], {x, 0, nn}], x]; f-fd (* Geoffrey Critzer, Oct 14 2012, after code given by Robert A. Russell in A000081 *)

Crossrefs

Cf. A001372 and A001373.

Sequence in context: A238435 A023425 A304173 * A360709 A090827 A109192

Adjacent sequences: A217893 A217894 A217895 * A217897 A217898 A217899

Keyword

nonn

Author

Geoffrey Critzer, Oct 14 2012

Status

approved