Euler’s Number
An infinite sequence of real numbers a(n) is defined for all integers n as follows:
![](https://projecteuler.net/project/images/p330_formula.gif)
For example,
a(0)=$frac{1}{1!}$+$frac{1}{2!}$+$frac{1}{3!}$+…=e-1
a(1)=$frac{1}{1!}$+$frac{1}{2!}$+$frac{1}{3!}$+…=e-1
a(2)=$frac{2e-3}{1!}$+$frac{e-1}{2!}$+$frac{1}{3!}$+…=$frac{7}{2}$e-6
with e = 2.7182818… being Euler’s constant.
It can be shown that a(n) is of the form $frac{A(n)e+B(n)}{n!}$ for integers A(n) and B(n).
For example a(10) = $frac{328161643 e − 652694486}{10!}$.
Find A(109) + B(109) and give your answer mod 77 777 777.
欧拉数
无穷实数序列a(n)按如下方式定义:
![](https://projecteuler.net/project/images/p330_formula.gif)
例如,
a(0)=$frac{1}{1!}$+$frac{1}{2!}$+$frac{1}{3!}$+…=e-1
a(1)=$frac{1}{1!}$+$frac{1}{2!}$+$frac{1}{3!}$+…=e-1
a(2)=$frac{2e-3}{1!}$+$frac{e-1}{2!}$+$frac{1}{3!}$+…=$frac{7}{2}$e-6
其中e = 2.7182818… 是欧拉常数。
可以发现a(n)总是可以表达为$frac{A(n)e+B(n)}{n!}$的形式,其中A(n)和B(n)均为整数。
例如a(10) = $frac{328161643 e − 652694486}{10!}$。
求A(109) + B(109),并将你的答案模77 777 777取余。
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