npm package: @stdlib/math-iter-sequences-factorials
Description: Create an iterator which generates a sequence of factorials.
Author: The Stdlib Authors
Latest version: 0.2.3

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# iterFactorialsSeq

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Create an iterator which generates a sequence of [factorials][oeis-a000142].

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

The [factorial][factorial-function] function may be defined as the product

<!-- <equation class="equation" label="eq:factorial_function" align="center" raw="n! = \prod_{k=1}^n k" alt="Factorial function definition"> -->

<div class="equation" align="center" data-raw-text="n! = \prod_{k=1}^n k" data-equation="eq:factorial_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/factorials/docs/img/equation_factorial_function.svg" alt="Factorial function definition">
    <br>
</div> -->

<!-- </equation> -->

or according to the recurrence relation

<!-- <equation class="equation" label="eq:factorial_recurrence_relation" align="center" raw="n! = \begin{cases}1 & \textrm{if } n = 0,\\(n-1)! \times n & \textrm{if } n > 1\end{cases}" alt="Factorial function recurrence relation"> -->

<!-- <div class="equation" align="center" data-raw-text="n! = \begin{cases}1 &amp; \textrm{if } n = 0,\\(n-1)! \times n &amp; \textrm{if } n &gt; 1\end{cases}" data-equation="eq:factorial_recurrence_relation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/factorials/docs/img/equation_factorial_recurrence_relation.svg" alt="Factorial function recurrence relation">
    <br>
</div> -->

<!-- </equation> -->

Following the convention for an [empty product][empty-product], in all definitions,

<!-- <equation class="equation" label="eq:zero_factorial" align="center" raw="0! = 1" alt="Zero factorial"> -->

<!-- <div class="equation" align="center" data-raw-text="0! = 1" data-equation="eq:zero_factorial">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/factorials/docs/img/equation_zero_factorial.svg" alt="Zero factorial">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-iter-sequences-factorials
```

</section>

<section class="usage">

## Usage

```javascript
var iterFactorialsSeq = require( '@stdlib/math-iter-sequences-factorials' );
```

#### iterFactorialsSeq( \[options] )

Returns an iterator which generates a sequence of factorials.

```javascript
var it = iterFactorialsSeq();
// returns <Object>

var v = it.next().value;
// returns 1

v = it.next().value;
// returns 1

v = it.next().value;
// returns 2

v = it.next().value;
// returns 6

v = it.next().value;
// returns 24

// ...
```

The returned iterator protocol-compliant object has the following properties:

-   **next**: function which returns an iterator protocol-compliant object containing the next iterated value (if one exists) assigned to a `value` property and a `done` property having a `boolean` value indicating whether the iterator is finished.
-   **return**: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.

The function supports the following `options`:

-   **iter**: number of iterations. Default: `1e308`.

By default, the function returns an infinite iterator (i.e., an iterator which never ends). To limit the number of iterations, set the `iter` option.

```javascript
var opts = {
    'iter': 2
};
var it = iterFactorialsSeq( opts );
// returns <Object>

var v = it.next().value;
// returns 1

v = it.next().value;
// returns 1

var bool = it.next().done;
// returns true
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

## Notes

-   If an environment supports `Symbol.iterator`, the returned iterator is iterable.

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var iterFactorialsSeq = require( '@stdlib/math-iter-sequences-factorials' );

// Create an iterator:
var opts = {
    'iter': 100
};
var it = iterFactorialsSeq( opts );

// Perform manual iteration...
var v;
while ( true ) {
    v = it.next();
    if ( v.done ) {
        break;
    }
    console.log( v.value );
}
```

</section>

<!-- /.examples -->

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<section class="references">

</section>

<!-- /.references -->

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<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-iter/special/factorial`][@stdlib/math/iter/special/factorial]</span><span class="delimiter">: </span><span class="description">create an iterator which evaluates the factorial function for each iterated value.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[deno-url]: https://github.com/stdlib-js/math-iter-sequences-factorials/tree/deno
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-iter-sequences-factorials/main/LICENSE

[oeis-a000142]: https://oeis.org/A000142

[factorial-function]: https://en.wikipedia.org/wiki/Factorial

[empty-product]: https://en.wikipedia.org/wiki/Empty_product

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[@stdlib/math/iter/special/factorial]: https://www.npmjs.com/package/@stdlib/math-iter-special-factorial

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