[LOJ#6268] 分拆數 [多項式求ln][多項式exp]

Link
LOJ - https://loj.ac/problem/6268

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$G(x)=\sum\limits_{n=0}^\infty p_r(n)x^n=\prod\limits_{k=1}^{n}(1+x^k+x^{2k}+\cdots+x^{\lfloor\frac{n}{k}\rfloor k})$
$\sum\limits_{n=0}^\infty x^{kn}=\frac{1}{1-x^k}$
$G(x)=\prod\limits_{k=1}^n\frac{1}{1-x^k}$
$\ln G(x)=\sum\limits_{k=1}^n-\ln(1-x^k)$
$\ln G(x)=\sum\limits_{k=1}^n\sum\limits_{r=0}^\infty\frac{x^{rk}}{r}$
$G(x)=e^{A(x)}$