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Say I have a polynomial like: 1+x^(n)+3x^(n+1)+3nx^(3n+4)

I want to extract the coefficient list {1,1,3,3n}.

I've been toying around with SeriesCoefficient and CoefficientList but they don't seem to work because the exponent $n$ is arbitrary.

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You could convert the sum of terms to a list of terms (using Apply), then replace all expressions like Power[x,_] with 1. This approach should return the list of coefficients of the polynomial despite arbitrary constants throughout.

eqn = 1 + x^(n) + 3 x^(n + 1) + 3 n x^(3 n + 4)
List @@ eqn /. Power[x, _] -> 1

Result:

{1, 1, 3, 3 n}
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