OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 14 2012
STATUS
approved