With this change, the β coefficients found in Cohen, Hubbard, and Oesterwinter (1973) can be computed as

Δ = GenerateFornberg[14, 14, 1, -# &];
δ[m_, n_, j_] := Δ[[m + 1, n + 1, j + 1]];
With[
 {n = 14},
 Table[
  Sum[
   ((-1)^(k - 1) (1 - 2^k) δ[k - 2, n - 2, j])/k!,
   {k, 2, n}],
  {j, 0, n - 2}]]

The common denominator is 1743565824000, and the numerators are:

9072652009253
-39726106418680
140544566352762
-344579280210120
613137294629235
-811345852376496
807012356281740
-602852367932304
333888089374395
-133228219027160
36262456774618
-6033724094760
463483373517

Please put the code to compute the Cohen et al. coefficients in some .wl file (either the same or a separate one). This can be done in a separate PR.