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'
forumTopicId: 301988
---

## Description
<section id='description'>

An infinite sequence of real numbers a(n) is defined for all integers n as follows:
<!-- TODO Use MathJax and re-write from projecteuler.net -->
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);

```

</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>