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Perhaps the following code is close to what you want:

With[{n = 4}, Sum[Binomial[n, r] b^r ** a^(n - r), {r, 0, n}]]
  /. {NonCommutativeMultiply -> Dot} // InputForm

with resulting output

1 . a^4 + 4*b . a^3 + 6*b^2 . a^2 + 4*b^3 . a + b^4 . 1