OFFSET
1,2
FORMULA
EXAMPLE
1,
2, 1,
4, 1, 2,
8, 3, 2, 6,
19, 5, 4, 6, 21,
53, 14, 10, 12, 21, 112,
209, 39, 24, 24, 42, 112, 853,
1253, 170, 72, 72, 84, 224, 853, 11117,
13599, 1083, 322, 210, 231, 448, 1706, 11117, 261080,
MATHEMATICA
nn=10; h[list_]:=Select[list, #>0&]; f[list_]:=Total[Table[list[[i]]*(i-1), {i, 1, Length[list]}]]; g[x_]:=Sum[NumberOfGraphs[n]x^n, {n, 0, nn}]; c[x_]:=Sum[a[n]x^n, {n, 0, nn}]; a[0]=1; sol=SolveAlways[g[x]==Normal[Series[Product[1/(1-x^i)^a[i], {i, 1, nn}], {x, 0, nn}]], x]; b=Drop[Flatten[Table[a[n], {n, 0, nn}]/.sol], 1]; Map[h, Drop[Transpose[Table[Map[f, CoefficientList[Series[(1/(1-y x^n)^b[[n]])Product[1/(1- x^i)^b[[i]], {i, 1, nn}](1-x^n)^b[[n]], {x, 0, nn}], {x, y}]], {n, 1, nn}]], 1]]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Mar 30 2013
STATUS
approved