Pari/GP, 48 bytes
The generating function of the sequence is:
$$\frac{(n-1)x^n}{x^{n+1}-2x+1}-\frac{1}{x-1}$$
(n,m)->Vec(x^n/((x^n-2)*x+1)*n---1/(x-1)+O(x^m))
alephalpha
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