@J.M. here is the code I use to implement EMS:
GenerateEM[n_] :=
Module[{a, b},
a = PadRight[CoefficientList[Series[x/(1 - Exp[-x]), {x, 0, n}], x], n + 1];
b = Table[Hold[D[#1, {#2, k}]] /. k -> i, {i, 0, n}];
ReleaseHold[Function[Evaluate[a.b]]]]
EM = GenerateEM[11]
LInt = {Integrate[#1, #2], #2} &
EMSum[f_, x_] := Collect[EM @@ LInt[f, x], x]