---
id: 5900f4b71000cf542c50ffc9
challengeType: 5
title: 'Problem 330: Euler''s Number'
---
## Description
An infinite sequence of real numbers a(n) is defined for all integers n as follows:
For example,a(0) =
11!
+
12!
+
13!
+ ... = e − 1
a(1) =
e − 11!
+
12!
+
13!
+ ... = 2e − 3
a(2) =
2e − 31!
+
e − 12!
+
13!
+ ... =
72
e − 6
with e = 2.7182818... being Euler's constant.
It can be shown that a(n) is of the form
A(n) e + B(n)n!
for integers A(n) and B(n).
For example a(10) =
328161643 e − 65269448610!
.
Find A(109) + B(109) and give your answer mod 77 777 777.
## Instructions
## Tests
```yml
tests:
- text: euler330() should return 15955822.
testString: assert.strictEqual(euler330(), 15955822, 'euler330() should return 15955822.');
```
## Challenge Seed
```js
function euler330() {
// Good luck!
return true;
}
euler330();
```