ASC(22)H（大数+推公式）

High Speed Trains

Time Limit: 4000/2000MS (Java/Others)Memory Limit: 128000/64000KB (Java/Others)

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Problem Description

      The kingdom of Flatland has n cities. Recently the king of Flatland visited Japan and was amazed by high speed trains Shinkansens going all around the country. Therefore he decided to build the system of high speed trains in Flatland.

      Each high speed train line will be bidirectional and connect exactly two different cities of Flatland. Although there is actually no need of high speed trains in Flatland, the king ordered that there must be at least one high speed train line from each city of Flatland.
      The minister of transportation told the king that there are several train system satisfying his requirements. The king was amazed by the fact and asked the minister to count the number of possible systems.
      Help the minister to calculate the number of train systems.

Input

      The input file contains one integer number n (2 ≤ n ≤ 100)

Output

      Output one integer number — the number of different train systems that can be arranged in Flatland.

Sample Input

4

Sample Output

41

题意：给出图的点数n，要求的是由这n个点能够构成多少种图，要满足每一个点至少有一条边相连，两点之间最多一条边。图能够不连通

思路：推公式题

            dp[n] = dp[n-1] * ( 2^(n-1) - 1 ) + C( n-1 , 1 ) * 2^(n-2) * dp[n-2] + C( n-1 , 2 ) * 2^(n-3) * dp[n-3] + ...... + C( n-1 , n-3 ) * 2^( 2 ) * dp[ 2 ] + 1

            要用大数