Link
LOJ - https://loj.ac/problem/6268
G ( x ) = ∑ n = 0 ∞ p r ( n ) x n = ∏ k = 1 n ( 1 + x k + x 2 k + ⋯ + x ⌊ n k ⌋ k ) 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}) G(x)=n=0∑∞pr(n)xn=k=1∏n(1+xk+x2k+⋯+x⌊kn⌋k)
∑ n = 0 ∞ x k n = 1 1 − x k \sum\limits_{n=0}^\infty x^{kn}=\frac{1}{1-x^k} n=0∑∞xkn=1−xk1
G ( x ) = ∏ k = 1 n 1 1 − x k G(x)=\prod\limits_{k=1}^n\frac{1}{1-x^k} G(x)=k=1∏n1−xk1
ln G ( x ) = ∑ k = 1 n − ln ( 1 − x k ) \ln G(x)=\sum\limits_{k=1}^n-\ln(1-x^k) lnG(x)=k=1∑n−ln(1−xk)
ln G ( x ) = ∑ k = 1 n ∑ r = 0 ∞ x r k r \ln G(x)=\sum\limits_{k=1}^n\sum\limits_{r=0}^\infty\frac{x^{rk}}{r} lnG(x)=k=1∑nr=0∑∞rxrk
G ( x ) = e A ( x ) G(x)=e^{A(x)} G(x)=eA(x)
![题解 P6268 【[SHOI2002]舞会】](/images/no-images.jpg)
