Urban Planning [polynomial, FIG communication count]

N points determined simple (no re-Loop-free side) to the number of non-connected graph, $ n <= 130000 $, $ mod 1004535809 $

F_i provided $ i $ denotes dots undirected FIG number, communicating FIG counting routine, block size enumeration communication station 1 is located

\begin{array}{rcl}
f_n&=&2^{C_n^2}-\sum\limits_{i=1}^{n-1}\binom{n-1}{i-1}f_i 2^{C_{n-i}^2}
\\f_n&=&2^{C_n^2}-(n-1)!\sum\limits_{i=1}^{n-1}\frac{f_i}{(i-1)!}\frac{2^{C_{n-i}^2}}{(n-i)!}
\\\frac{f_n}{(n-1)!}&=&\frac{2^{C_n^2}}{(n-1)!}-\sum\limits_{i=1}^{n-1}\frac{f_i}{(i-1)!}\frac{2^{C_{n-i}^2}}{(n-i)!}
\end{array}

设$F_i=\frac{f_i}{(i-1)!},G_i=\frac{2^{C_i^2}}{i!},F_1=1,G_0=0$

Have

\begin{array}{rcl}
F_n&=&\frac{2^{C_n^2}}{(n-1)!}-\sum\limits_{i=0}^{n}F_iG{n-i}
\end{array}

Found the back of their own in the form of roll your own, you can divide and conquer NTT. $ \ Theta (nlog ^ 2n) $

All information has been collected the leaf nodes required that point, the preceding item taken into account, update others.

The similar items together, can be referred to outside the proposed $ \ sum $ to find value, set polynomial, constructed in the form of convolution.

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Origin www.cnblogs.com/hzoi-yzh/p/12038683.html