Math Stackexchange 810586

G[0, x_] := Sum[u[i] x^i, {i, 0, 10}]
G[k_, x_] := (c^k/(c^k - 1) - 1/(c^k - 1) x) G[k - 1, x]
formula[h_] := Sum[c^((p^2 + p)/2)/((\!\(
\*UnderoverscriptBox[\(\[Product]\), \(i = 1\), \(p\)]\((
\*SuperscriptBox[\(c\), \(i\)] - 1)\)\)) (\!\(
\*UnderoverscriptBox[\(\[Product]\), \(i = 1\), \(h - p\)]\((1 -
\*SuperscriptBox[\(c\), \(i\)])\)\))) u[p], {p, 0, h}];
Table[formula[h] /.
   u[i_] ->
    If[i < 10, {u0, u1, u2, u3, u4, u5, u6, u7, u8}[[i + 1]]] /.
  c -> 4, {h, 1, 8}]
Table[Coefficient[G[h, x], x, h] /.
   u[i_] ->
    If[i < 10, {u0, u1, u2, u3, u4, u5, u6, u7, u8}[[i + 1]], 0] /.
  c -> 4, {h, 1, 8}]