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For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.

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Binomial expansion for noncommutative operator

Is it possible to find a closed formula for $(A^\dagger -kA)^n$ with $[A,A^\dagger]=1$ ? I am looking for the normal ordinate form: $\sum (A)^{n-j}(A^\dagger)^j$— possibly something to do with the co …