OFFSET
1,5
FORMULA
O.g.f.: Product_n>=1 (1+ y*x^n)^A000055(n).
EXAMPLE
1,
1,
1, 1,
2, 1,
3, 3,
6, 5, 1,
11, 11, 2,
23, 21, 5,
47, 46, 12,
106, 96, 27, 2
MATHEMATICA
nn = 20; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol = SolveAlways[0 == Series[f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}], x]; r[x_] := Sum[a[n] x^n, {n, 0, nn}] /. sol; b = Drop[Flatten[CoefficientList[Series[r[x] - 1/2 (r[x]^2 - r[x^2]), {x, 0, nn}], x]], 1]; Map[Select[#, # > 0 &] &, Drop[CoefficientList[
Series[Product[(1 + y x^n)^b[[n]], {n, 1, nn}], {x, 0, nn}], {x, y}], 1]] // Grid
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jul 09 2020
STATUS
approved