Problem 380
Amazing Mazes!
An m×n maze is an m×n rectangular grid with walls placed between grid cells such that there is exactly one path from the top-left square to any other square. The following are examples of a 9×12 maze and a 15×20 maze:
Let C(m,n) be the number of distinct m×n mazes. Mazes which can be formed by rotation and reflection from another maze are considered distinct.
It can be verified that C(1,1) = 1, C(2,2) = 4, C(3,4) = 2415, and C(9,12) = 2.5720e46 (in scientific notation rounded to 5 significant digits).
Find C(100,500) and write your answer in scientific notation rounded to 5 significant digits.
When giving your answer, use a lowercase e to separate mantissa and exponent. E.g. if the answer is 1234567891011 then the answer format would be 1.2346e12.
神奇的迷宫！
将一个m×n的长方形网格的部分方格之间用墙隔开，使得从左上角的方格出发恰好只有一条路到达其它任意方格，就构建了一个m×n迷宫。如下所示是一个9×12迷宫和一个15×20迷宫：
记C(m,n)是不同的m×n迷宫的数目。如果一个迷宫可以通过旋转或翻转变为另一个，这两个迷宫仍然被认为是不同的。
可以验证C(1,1) = 1，C(2,2) = 4，C(3,4) = 2415，以及C(9,12) = 2.5720e46（用科学计数法表示，四舍五入至5位有效数字）。
求C(100,500)，并将你的答案用科学计数法表示，四舍五入至5位有效数字。
在给出你的答案时，用一个小写字母e隔开尾数和指数。例如，如果精确答案是1234567891011，那么提交的答案格式应当为1.2346e12。