freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-330-eulers-number.english.md

---
id: 5900f4b71000cf542c50ffc9
challengeType: 5
title: 'Problem 330: Euler''s Number'
---

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler330()</code> should return 15955822.
    testString: assert.strictEqual(euler330(), 15955822, '<code>euler330()</code> should return 15955822.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler330() {
  // Good luck!
  return true;
}

euler330();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>