Clear[t, n, k, i, nn, x] coeff = {1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}; nn = Length[coeff] cc = Range[nn]*0 + 1; Monitor[Do[ Clear[t]; t[n_, 1] := t[n, 1] = cc[[n]]; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}] - Sum[t[n - i, k], {i, 1, k - 1}], 0]; A4 = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]; A5 = A4[[1 ;; nn - 1]]; A5 = Prepend[A5, ConstantArray[0, nn]]; cc = Total[ Table[coeff[[n]]*MatrixPower[A5, n - 1][[All, 1]], {n, 1, nn}]]; , {i, 1, nn}], i] cc CoefficientList[Series[(1 + x)/(1 + 2*x), {x, 0, nn - 1}], x] Flatten[{1, Table[(-(-2)^(n - 1)), {n, 1, 28 - 1}]}]